2018-2019
Quick Links: Quiz corrections form Trig Flashcards Desmos Online Graphing Calculator
Unit Circle Khan Academy Review of Unit Circle Trig Values
For Deltamath.com Teacher Code: 378779; pick your appropriate period.
End of Year Exam Schedule; SAT Practice Tests
Thursday 6/13-Friday 6/14: Warm-Up
Wednesday 6/12: Warm-up; continue Scavenger Hunt Review-- medium, hard. Optional Deltamath-- Even and Odd Functions, The Discriminant
Tuesday 6/11: Warm-up; Scavenger Hunt Review-- medium, hard
Monday 6/10: Review Packet (solutions) ****Typo on #9-- can you spot it.
Friday 6/7: Good stuff to know (solutions); Delta Math-- trig properties review
Thursday 6/6: Delta Math-- unit circle review
Monday 6/3-Tuesday 6/4: Warm-Up; Quarterfinal Review (solutions)
Friday 5/31: Warm-up, Quarterfinal Review (solutions)
Thursday 5/30: Problem Set 4.4 (quia)
Wednesday 5/29: 16.4b The Derivative (solutions)
Tuesday 5/28: 16.4 The Derivative (solution) example video- derivative of a quadratic; another example-- rational function
(16.4) pp874-875 #3-4, 11, 15, 17, 20, 29-30, 35, 40. (due FRI)
3-4, 11. limit as h approaches 0 of [f(x + h) – f(x)]/h. The second derivative is the derivative of the first derivative.
15, 17. Get rid of complex fractions by multiplying top and bottom by LCD.
20. congugate
29. 24, The function is not differentiable at 24 (there’s no left hand limit there).
30. The function is differentiable at all points on the domain.
35. Find the derivative and set it equal to -4.
40. Same thing as usual—get the h’s to cancel out. check 16.4 hwk
Friday 5/24: Delta Math: Tangent Lines
Thursday 5/23: 16.3 Problems (pd9 16.3 Tangent to a Curve (solutions))
Tuesday 5/21-Wednesday 5/22: Warm-up-- Down the Shore; 16.3 Tangent to a Curve (solutions)
Assign: (16.3) pp869-870 #3, 4, 8-10, 18, 26, 34. (due Friday)
For all of these use the difference quotient:
limit as x approaches c of [f(x) – f(c)]/(x – c).
(c, f(c)) is the ordered pair given in the problem.
All of these limits are indeterminate forms, “0/0”, which can easily be handled by factoring.
18. see Ex3, p867
26. Find the slope using the difference quotient:
limit as x approaches c of [f(x) – f(c)]/(x – c).
34. avg velocity = slope formula, instantaneous velocity = limit
check 16.3 hwk solutions: part 1, part 2
Monday 5/20: Quiz-- limits
Friday 5/17: Limit Problems (solutions) Quiz Monday 5/20
Thursday 5/16: Warm-up; DeltaMath--limits of functions ; finish 16.2 hwk (assigned Mon)
Wednesday 5/15: Warm-up; DeltaMath--limits of functions
Tuesday 5/14: Warm-Up; Finish 16.2 Problem Set--limits (check solutions); 4.3 Problem Set--limits (quia)
Monday 5/13: Desmos Activity: limits and continuity; 16.2 Problem Set--limits (check solutions)
Assign: (16.2) pp863-864 #1-16, 18-20, 21-29, 32-34, 41-42 (due Friday)
Before we begin I cannot reiterate enough: LIMITS ARE Y-VALUES!!!!!
#1-9. Just plug-in the values. Yes, it’s that easy! Why can you do this? Because these functions are continuous at these values.
10-13. Factor and cancel first.
14-16. For limits at infinity compare the degrees (highest power) of the numerator and denominator. These are the same as horizontal asymptotes.
18-20. There are many acceptable answers for these.
21-27. All are indeterminate forms -- “0/0”. Factor and cancel first.
28-29. Divide everything by x2.
32-34. Don’t get intimidated by these piecewise functions. Draw the graph. For 33 and 34 factor and cancel first.
41-42. To be continuous, check the end points of each interval. For instance, in #42, let x = 3 for the top 2 equations: 3 – 3 = sqrt (a – 32). Now solve for a. In the same way, let x = -3 in the 2nd and 3rd equations and set them equal.
check 16.2 hwk (page 1); (page 2)
Friday 5/10: 16.2 Limit Theorems
Thursday 5/9: 16.1 Limit of a Function
Assign: (16.1) pp857-858 #1-14, 17-30, 33-36, 41-44.
#1-6. These are actually 4 part questions: a) left hand limit as x approaches c, b) right hand limit as x approaches c, c) limit at c, d) f(c).
REMEMBER—LIMITS ARE y-values!!!!!
7-10. Again, limits are y-values.
11-14. “plug-in”
17-25. These are all continuous functions; remember that polynomials are continuous everywhere. So, just plug-in the values. Yes, it’s that easy!
26. The bottom of a fraction gets really big.
27-28. Polynomials = continuous = plug-in.
29. Use the top part of the function and factor.
30. Plug into both sides of the function.
33-36. Graph
41-44. Plug-in. check 16.1 HWK
Tuesday 5/7: 13.7 Problems (solutions)
Monday 5/6: 13.7 Sums of Infinite Series
Assign: (sect 13.7) pp725-727 #6-13, 16-17, 29, 31, 34 (due Wed)
6-13. Infinite Geometric Series converge when -1 < r < 1.
They converge to S = a/(1 – r).
16. a = 0.45, r = .01
17. a = .9, r = .1
29. This question is worded poorly. What they actually mean here is the distance (both up and down) right up until the ball hits the ground for the 5th time. Draw a picture. You get 36 + 2*36(.7) + 2*36(.7)2 + 2*36(.7)3 + 2*36(.7)4 = 163.6632 [Note that the 2s here account for the up and down.]
31. This is theoretically what we’re hoping for when we “stimulate” the economy. Since 90% of what’s received gets spent, this is an infinite geometric series with r = 0.90. Be careful, the first “spending” is .90(10 billion) = 9 billion = a1 = a. Now, use S = a/(1 – r).
34. Use S = a/(1 – r) and solve for r. Then write out the series, or better yet, express your answer in sigma notation.
Friday 5/3 (Physics Trip): Review Quiz; catch-up on assignments.
Thursday 5/2: Quiz
Wednesday 5/1: Review Problems (solutions); Quiz Thursday.
Tuesday 4/30: Warm-Up; quick DeltaMath-- limits!; Quiz Thursday.
Monday 4/29: 13.6 Limits of Sequences
Assign: (sect 13.6) pp718-719 #4-16 (all), 26-28. (due Wed)
4. Geometric
5. divide numerator and denominator by n.
6. divide numerator and denominator by n2.
7. Write out a few terms.
8. divide numerator and denominator by n.
9. divide numerator and denominator by n2.
10-11. Write out a few terms.
12. Geometric
13. divide numerator and denominator by n5.
14. divide numerator and denominator by n8.
15. divide numerator and denominator by n5.
16. Does the sequence approach a specific value?
26. alternates
27. Geometric
28. What does r need to be to make each term decrease? check 13.6 solutions
Friday 4/26: Problem Set 4.2 (Series)
Thursday 4/25: Finish 13.5 Binomial Theorem (solutions); deltamath-- series.
Wednesday 4/24: 13.5 Binomial Theorem (solutions)
Assign: (sect 13.5) pp712-713 #5, 7, 14, 18, 25, 27, 32. (due Fri)
5. n!/[r! (n – r)!]
7. For binomial coefficients use the 9th row of Pascal’s Triangle: 1, 8, …
14. Try it for n = 7 and r = 4 and see what happens. Easy proof.
18, 25, 27. see Ex6, p711
32. see Ex6, p711, and remember i2 = -1 check 13.5 solutions
Tuesday 4/23: 13.1-3 Problems (check solutions)
Monday 4/22: 13.3 Series
Assign: (sect 13.3) pp695-697 #4-6, 13, 18, 20, 34, 37, 45.
4-6. Write the explicit formula for the nth term and then slap a sigma in front of it.
13. Add up the first 12 terms. Can you do this quickly by formula (p692)?
18. Add up the first 8 terms. Can you do this quickly by formula (p693)?
20. Geometric series. Use the formula on p693.
34. Arithmetic series. Use the formula on p692.
37. Geometric series. Use the formula on p693.
45. Arithmetic series. Use the formula on p692. check 13.3 HWK
Friday 4/12: Problem Set 4.1 (quia)
Wednesday 4/10- Thursday 4/11: 13.2 Arithmetic & Geometric Sequences
Assign: (sect 13.2) p687 #1, 4, 5, 7, 9, 16, 26, 30, 31, 34. (due Fri)
#1, 4, 5, 7, 9. Remember arithmetic means you’re adding the same thing every time. The thing you’re adding is d, the common difference. Geometric means you’re multiplying the same thing every time. The thing you’re multiplying is r, the common ratio.
16. The general form of an arithmetic sequence is an = a0 + d(n-1).
26. Try it. See what happens.
30. The general form of a geometric sequence is an = a0*rn-1. Remember, appreciating by 5% is the same as multiplying by 1.05
31. Restaurant A is arithmetic, restaurant B is geometric.
34. Geometric. The general form of a geometric sequence is an = a0*rn-1. check 13.2 Hwk solutions
Tuesday 4/9: deltamath-- Sequences; then finish text homework (below)
Monday 4/8: 13.1 Sequences
Assign: (sect 13.1) pp677-680 #4, 9, 11, 13, 23, 34, 38, 40, 41. (due Wed)
4. Plug in the integers 1, 2, … , 5
9. What’s the pattern in the denominator?
11. Start with 24 and what do you do each time?
13. Start with a0 = -12. an = ?
23. Write out the first few terms to get you started.
34. 2 is the first prime. 1 is neither prime nor composite. 2 is also the only even prime.
38. I’m confused too. It’s just the Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 21.
40. Start with b0 = 200. bn = ? b5 = ?
41. Start with h0 = 6. Remember that an increase of 12% is the same as multiplying by 1.12.
check 13.1 solutions
Friday 4/5: SAT day-- let's take a break from precalc and look at some challenging SAT problems.
Wednesday 4/3-Thursday 4/4: Quarterfinal
Tuesday 4/2: Warm-up
Monday 4/1: warm-up; Big Review packet (check solutions); 3.4 Quia Problem Set
Friday 3/29: Big Review packet (check solutions); 3.4 Quia Problem Set
Thursday 3/28: check 9.6 HWK; Exponent and Log Problem Set (check solutions)
Wednesday 3/27: Quiz Review
Tuesday 3/26: Exponent and Log Problem Set
Monday 3/25: 9.6 Exponential Modeling; 9.4-9.6 Problems
(sect 9.6) pp478-479 Practice Exercises #5-6, 8-10, 23-25. (due Wed)
A good thing to keep in mind in all of these problems is that the subscript 0 means the amount at time = 0 or the original amount. For example P0 would mean original population.
5-6, 8. Plug in what you’re given, ln x “undoes” ex.
9. Use the formula A = A0(2)-t/5570. (see p 477, Example 3)
10. Plug in what you’re given, ln x “undoes” ex.
23. A good idea here is to let 1981 be year t = 0, so 1983 would be year t = 2. P0 = 23,153.
24. Let N = 70 and solve.
25. In calculator: y1 = 5e^(-0.4x); y2 = 2.25. Find the x where these two graphs intersect. (get a good window). Then do the same with y1 = 5e^(-0.4x) and y3 = 0.5
Thursday 3/21: 9.5 Exponential Equations
Assign: (sect 9.5) pp472-474 #7, 9, 11, 12, 21, 32, 36, 38. (due Mon) check 9.5 hwk
7, 9. Isolate exponential and log both sides.
11-12. Multiply by ex .
21, 32. Use A = Pert.
36. Use A = P(1 + r/n)nt
38. Use A = Pert.
Wednesday 3/20: DeltaMath: logarithms; check 9.3 HWK and 9.4 HWK
Tuesday 3/19: 9.1-9.4 Problems (check solutions)
Monday 3/18: 9.4 Properties of Logarithms
Assign: (sect 9.4) pp464-466 #21-26, 31-35, 37-38. (due Wed)
21-24. Use log properties on p461 of text.
25. Remember that ln e = 1 and ln en = n
26. log 10n = n
31-33. Again, use the log properties to get a single logarithm and then use “da, da, da,…” to change it to an exponential equation.
34. Plug in. You’re solving for P.
35. Plug in.
37. Use the change of base formula: logb x=(log x)/(log b) and also use the fact that log 10n = n. Remember that 0.1 = 10-1.
38. Use the change of base formula: logb x=(log x)/(log b) and also use the fact that log 10n = n. Remember that 100 = 102.
Thursday 3/14: desmos activity: exponentials
Wednesday 3/13: 9.3 Logarithms (solns)
Assign: (sect 9.3) p458 #5-9, 15, 18, 28, 32, 40-43, 45. (due Mon 3/18)
5-7. Change logs to exponents using “da, da, da, ….”
8. e is the base of the natural logarithm.
9. You’re graphing 3y=x
15. too easy
18. logb x=(log x)/(log b)
28. graph ‘em. what do you notice?
32. plug in
40-43. These are a little tough, but you can do them. The general equation is y = logb(x – c)+d where c is the vertical asymptote. You can fill in the other ordered pairs to find b and d.
45. You can actually just plug in.
Monday 3/11-Tuesday 3/12: 3.3 Problem Set (quia)-- exponential functions
Friday 3/8: 9.2b Exponential Models (solutions)
Thursday 3/7: 9.2 Properties of Exponential Functions (solutions); 9.2a Exponential Models (solutions)
Wednesday 3/6: 9.1 Intro to Exponential Functions (solutions)
Assign: (sect 9.2) Practice Exercises pp450-452 #14-20, 23, 25, 30-32, 38-39. [All graphs are rough sketches—figure out where the asymptotes are.] (due Tuesday 3/12)
14-15. Get a common base. There is no need to use logarithms on these.
16. Use the zero product property.
17. Factor and use the zero product property.
18. Use the equation and make sure to represent the rate of increase as a decimal.
19. Depreciation decreases to value of the car. r = -0.20 for this problem.
20. A simple plug-in problem.
23. Graph y = 2x and use transformations. Label key points and the asymptote. Check with a calculator.
25. Graph y = 4x and use transformations. Label key points and the asymptote. Check with a calculator.
30-31. Factor out a GCF first.
32. What does the power have to be to get a 1 on the right side?
38. A simple plug-in.
39. Review problem. If you have a perfect square trinomial, the discriminant = 0.
*check 9.2 hwk solns: part 1, part 2
Tuesday 3/5: 7.7 Quiz
Monday 3/4: Pre-quiz warm-up. (solutions) Review atpac
Monday 3/4: Quiz helpful video on asymptotes
Friday 3/1: AT-PAC #5
Thursday 2/28: Factoring Day; deltamath.com-- factoring review
Wednesday 2/27: check 7.7 hwk; 7.7 Review Problems (check solutions); quiz Friday
Tuesday 2/26: Function Scavenger Hunt
Monday 2/25: 7.7 Radical Functions
Practice Exercises (sect 7.7) pp374-375 #11, 12, 15, 19, 22-23, 35-36. (due Wed)
11. Square both sides. Check for extraneous solutions.
12. sqrt(a)sqrt(b)=sqrt (ab)
15. isolate radical and cube both sides.
19. V = (1/3)pi*r^2*h
22-23. Get rid of one radical at a time. You’ll end up squaring both sides twice.
35. Square both sides to get rid of the 4th root.
36. No big deal…. c is just a number.
Friday 2/21: Warm-up (solutions); finish Problem Set 3.2 (quia) and Practice Exercises (sect 7.6) pp368-370 #8, 10, 12, 36, 39, 45. (hints below)
Thursday 2/20: Warm-Up (solutions); Problem Set 3.2 (quia)
Tuesday 2/19: 7.6 Rational Functions; How do we get asymptotes?
videos: How to find horizontal asymptotes. How to find vertical asymptotes.
Practice Exercises (sect 7.6) pp368-370 #8, 10, 12, 36, 39, 45. (due Fri)
8. It’s the greatest integer function—MATH-NUM-INT (on TI-84). At what x-values do you “jump”?
10. It’s a piecewise function. Make sure to check x = 4.
12. What happens at x = 5?
36. What happens at x = 3. Find intercepts—y-int (set x = 0), x-int (set numerator = 0). Horizontal asymptote? Compare the degrees of numerator and denominator—if tied, divide the leading coefficients.
39. What happens at x = -1, and x = 6. Find intercepts—y-int (set x = 0), x-int (set numerator = 0). Compare the degrees of numerator and denominator.
45. Horizontal asymptote? Compare the degrees of numerator and denominator—if tied, divide the leading coefficients. Vertical asymptote—zeros out the denominator, but not the numerator.
Wednesday 2/13: 7.5 Practice (solutions)
Tuesday 2/12: Snow/Ice/Slush... yuck.
Monday 2/11: 7.5 Descartes Rule (solutions)
Assign: Practice Exercises (sect 7.5) pp361-363 #32, 33, 36-38, 43-44, 51-52. (due Tues 2/19)
32-33. Graph and zoom in. You can also use CALC—ZERO (2nd TRACE).
36-37. see p 357
38. There are a few reasons. You could’ve answered this before this chapter.
43. Graph and zoom in. You can also use CALC—ZERO (2nd TRACE).
44. x(x+2)(x+4)=43. Solve—use your graphing calculator to find a root.
51. Descartes’ Rule of Signs
52. Graph and zoom in. You can also use CALC—ZERO (2nd TRACE).
Wednesday 2/6-Thursday 2/7: 7.4 Review problems (solutions) Quiz Fri.
Tuesday 2/5: 7.4 problems (solutions); Problem Set 3.1 (quia)
Monday 2/4: 7.4 Fundamental Theorem of Algebra (solutions) Quiz Fri; check 7.3 hwk; 7.3 hwk #43
An nth degree polynomial will have n rational zeros.
Kush's Thm: For a quadratic ax^2 + bx + c, the sum of the zeros is -(b/a) and the product of the zeros is c/a.
Assign: Practice Exercises (sect 7.4) pp353-355 #24, 26, 28, 34 (use calc), 37-38, 46. (due Wed)
Hints: 24, 26, 28. Remember that Complex Roots and Radical Roots come in conjugate pairs. (i.e. If -1- i is a root, then -1 + i is a root.)
34. Use your calculator to find the lowest point of the graph between x = 0 and x = 6. Adjust your window so you can see the whole graph.
37, 38. Use the theorem (Kush’s Thm) about the sum of the zeros and the product of the zeros of a quadratic.
46. Set equal to zero and solve. check 7.4 HWK
Friday 2/1: Finish 7.3 Rational Zeros Theorem (solutions); 7.2 Quick Polynomial Graphs part2 (solutions)
Thursday 1/31: 7.3 Rational Zeros Theorem
Hwk (due Mon): Practice Exercises (sect 7.3) pp347-348 #22, 24, 26, 27, 34, 36, 38, 40, 43—5 solutions to this one!
22, 24, 26. Synthetic division. Guess and check until you get a remainder of zero. Get down to a quadratic so you can factor.
27. Draw a good picture. Then write an equation for volume.
34. Same stuff. Synthetic division.
36, 38. Graph it if you get stuck finding a zero.
40. Similar to what we did in the last section: 3 is your multiplier and -1 is the remainder.
43. Replace cos2x with 1 – sin2x.
Wednesday 1/30: 7.2 Quick Polynomial Graphing; Deltamath assignment-- Polynomial Graphs (pds 7/8, 10 play catch-up)
Tuesday 1/29 (early dismisssal): 7.2 Warm-up and Notes; 7.2 Graphing Polynomials
Good stuff to know about polynomials: Webpage that may help; video: graphing polynomials
1. Polynomials are smooth CONTINUOUS curves. The domain is all reals.
2. nth degree polynomials can have up to n real zeros. They have exactly n zeros if we include complex zeros and multiplicities.
3. nth degree polynomials can have up to n - 1 extrema. Extrema are max and min points.
4. A horizontal inflection point is not an extrema.
5. Even degree polynomials have the shape of a "touchdown"; odd degree polynomials are shaped like "stayin' alive."
6. Zeros are also known as roots. These are x-intercepts for real zeros.
7. Extrema are minimum and maximum points. We usually call these relative minimums and relative maximums.
8. End behavior: Even degree functions start high left and end high right (like y = x^2, a parabola). Of course a negative in front changes the shape to an upside down parabola, so it would start low left and end low right. Odd degree functions start low left and end high right (like y =x^3, the basic cubic function). And again, a negative in front would flip the graph in the x-axis.
Assign: Practice Exercises (sect 7.2) pp340-342 #10, 12, 18-20, 22, 25-29, 35, 37, 45. (due Thurs)
Hints to homework assignment:
10, 12. Just a “rough sketch” of the graph. The multiplicity determines how the graph “cuts though” the x-axis.
18-19. Remember, Even: f(-x) = f(x), symmetric in y-axis; Odd: f(-x) = -f(x), symmetric in the origin. NOTE: This is not the same as even and odd degree.
20. How many extrema does y = x4 have?
22. Draw it.
25-26. Work backwards. Leave your answer in factored form.
27-29. No problem. You’ve got this.
35, 37. This is a way to use the graph to factor a polynomial.
45. Good Luck! check 7.2 hwk solutions
Monday 1/28: Synthetic Division and the Remainder and Factor Theorems (solutions); homework problems; (homework answers)
Friday 1/25: Dividing Polynomials
Quarterfinal: Wed 1/23 (No Calculator) & Thurs 1/24 (Calculator allowed) Review Problems (solutions)
Thursday 1/17- Tuesday 1/22: Review Problems (solutions)
Wednesday 1/16: Quizlet live, quiz review, try more trig equations
Monday 1/14-Tuesday 1/15: 6.5 Solving Trig Equations Assign: #1-5, 16-20 on handout.
Solutions to #1-15 and #16-30. need help? video
Friday 1/11: Quiz
Thursday 1/10: 6.4 Product/Sum Identities (solutions)
Assign: Practice Exercises (sect 6.4) pp309-310 #3, 5, 8, 11, 14, 27; p310 Review #1-3. (due Mon)
3, 5, 8. Use the identities on p306.
11, 14. Use the identities on p307
27. Start with the right side and use the identities on p287.
Review Problems
1. Periodic function is defined on p182
2. Continuous means there is no “break” in the graph. Functions with vertical asymptotes are not continuous.
3. Don’t use a calculator.
6.4 hwk solutions-- part 1, part 2
Wednesday 1/9: 2.4 Problem Set (quia); check 6.3 hwk
Tuesday 1/8: 6.3 Extra Practice Problems-- in-class assignment, check solutions. Hand back and check 6.1 Practice Problems.
Monday 1/7: 6.3 Double Angle Identities (solutions)
Double Angle identities are for problems of the form sin(2α), cos(2α), tan(2α).
Half Angle identities are for problems of the form sin(α/2), cos(α/2), tan(α/2).
Practice Exercises (sect 6.3) pp302-305 #3, 5, 9, 11, 15, 17, 19. (due Wed)
Hwk Hints:
3. cos ((7pi/4)/2)
5. tan 11pi/8 = tan 3pi/8 = tan ((3pi/4)/2)
9. Draw a 4th Quadrant reference triangle.
11. Draw a 2nd Quadrant reference triangle.
15. Draw a 4th Quadrant reference triangle.
17. Draw a 4th Quadrant reference triangle.
19. θ is in the 3rd Quadrant, so θ/2 is in the 2nd Quadrant.
Friday 1/4: 6.1 Problems (group or individual work); check 6.1 hwk
Thursday 1/3: 6.1 More Practice (solutions); finish hwk (below).
Wednesday 1/2/19: 6.1 Sum and Difference Identities (solutions)
website (with proofs & examples); video of sin 195°
Assign: Practice Exercises (sect 6.1) pp290-292 #17-21, 23-25, 33-35 (due Fri)
17-20. Use the sum and difference identities.
19. 375 is coterminal with 15. sin 375 = sin 15 = sin (45-30)
21. 405 is coterminal with 45. EASY PROBLEM!
23-25, 33-35. Draw reference triangles and then use the sum and difference identities.
Tuesday 12/18- Thursday 12/20: 5.5 Areas of Triangles
pp276-279 (sect 5.5) Practice Exercises #11, 12, 17, 20, 22, 27, 29, 30, 31, 35, 39, 41, 49, 51, 53. (due Fri)
11. Area of a segment = Area of a sector – Area of triangle. Area of a sector = ½ r2 θ, when θ is in RAD
12. Area of a sector = (θ/360)pi*r2, when θ is in DEG.
17. Use Heron’s Formula to find the area, then use A = ½ bh and use t as the base to find the altitude to RS.
20. Use Heron’s Formula.
22. Divide into triangles and use ½ absinC.
27. Use ½ absinC backwards.
29. Connect B to D and find the area of each triangle.
30. Divide hexagon into 6 congruent (and equilateral) triangles.
31. Divide pentagon into 5 congruent triangles and use ½ absinC.
35. Area of a sector = (θ/360)pi*r2, when θ is in DEG.
39. Triangle – ½ circle. Each of those sectors is a 1/6 of a circle.
41. 6-8-10 right triangle.
49. Draw the radius from the center to a corner point of one of the crosses.
51. Find the square – the quarter of a circle.
53. Use a 30-60-90 triangle to find the radius. check 5.5 HWK: part 1, part 2
Monday 12/17: Quiz: Laws of Triangles
Friday 12/14: Appointment Calendar Activity Quiz Monday 12/17. Check 5.3 hwk and 5.4 hwk
Thursday 12/13: Prove the Law of Cosines; Quia 2.3 Problem Set-- Collins classes, Cavanaugh classes; Quiz Monday 12/17. Check 5.3 hwk and 5.4 hwk
Wednesday 12/12: 5.4 Problems (check solutions), check 5.3 HWK
Tuesday 12/11: 5.4 Law of Cosines (solutions)
Section 5-3: pp261-262 (sect 5.3) #23-25, 29, 35, 37 (due Wed), hints below Monday
Section 5-4: pp269-271 (sect 5.4) Practice Exercises #7, 9, 13, 17, 26, 29, 31, 37 (due Thurs)
7. Once you get an angle with the law of cosines, you can use the law of sines.
9. Use law of cosines, then law of sines.
13. Review problem.
17. Law of cosines.
26. You’re looking for the angle opposite 9.3
29. The angle between them is 59 degrees.
31. The angle at home plate (with pitcher and third base) is 45 degrees.
37. Draw a good diagram. check 5.4 hwk.
Monday 12/10: 5.3 The Ambiguous Case (solutions)-- video
classwork: 5.2 Problems (solutions)-- some word problems with Law of Sines and Right Triangle Trig;
Section 5-3: pp261-262 (sect 5.3) #23-25, 29, 35, 37 (due Wed)
23-24. Use sin 50 = x/31 to find the leg of the triangle. Will a 26 ft beam fit here?
25. Law of Sines
29. Solve for angle C using Law of Sines. Your calculator will give you a first quadrant angle (between 0 and 90), find a second quadrant angle (between 90 and 180) that also works for the smaller triangle.
35. Law of Sines
37. Draw a good picture. Remember that angle of depression and angle of elevation are congruent (alternate interior angles). check 5.3 HWK
Friday 12/7: Law of Sines Applications (solutions)
Thursday 12/6: Check solutions to right traingle trig problems. The Law of Sines (solutions)
Section 5-2: pp254-256 (sect 5.2) #3, 6, 9, 15, 22, 24, 27, 30, 41, 43. (due Monday)
Hints:
3, 6, 9. Use sinA/a = sin B/b = sinC/c
15. Draw a good picture.
22. AAA?
24. Find the 3rd angle first.
27. Again, start with a good diagram.
30. Fill in all angles first.
41. Tricky—don’t find theta! Try to get the other angle first!!!!!
43. Work with 1 triangle at a time.
check 5.2 hwk solutions
Wednesday 12/5: 5.1 Right Triangle Trig Applications (check solutions). Finish for homework.
Have you finished 2.2 Problem Set (quia)? It should be finished by now.
Tuesday 12/4: Quiz, then start 5.1 Right Triangle Trig Applications (check solutions)
Monday 12/3: 4.6 Review Problems (check solutions)
Friday 11/30: 2.2 Problem Set (quia); check 4.6 hwk. Quiz Tuesday
Thursday 11/29: Appointment Review
Wednesday 11/28: 4.6 Other Inverse Trig Functions (solutions) video-- inverse trig functions check 4.5 hwk
Section 4-6: Practice Exercises pp226-228 #1-3, 5-11 (odds), 12-18, 20-23, 28-29, 32, 39, 47. (due Fri)
1-3. Work backwards.
5. cos-1(1/9.7)=
7. see #5
9. Easy, but get into DEG mode.
11. see #5 and use DEG mode.
12. tan pi = 0, Arctan 0 = 0.
13-15. Easy—they just cancel out.
16-18. Like granny says, use a reference triangle.
20-22. Again, reference triangle.
23. Graph Tan-1x and then move it up 3 units.
28. Graph Csc-1x and then reflect all the negative y-values in the x-axis. In other words, any part of the graph below the x-axis gets reflected above the x-axis. Absolute value takes the negatives and makes them positives!
29. Any consecutive odd pi/2’s, like (pi/2, 3pi/2).
32. Plug in all the values and then use Tan-1 to solve for theta.
39. Reference Triangle
47. Reference Triangle
Tuesday 11/27: Inverse Trig handout #2 (solutions) classwork: deltamath.com -- Trig Review
Monday 11/26 (The push to Christmas starts now!): Inverse Trig Functions: Sine and Cosine (solutions)
Homework: Section 4-5: Practice Exercises p220-221 #1-6, 11-13, 15-17, 20, 24, 29-31, 35, 43-44. (due Wed)
Hints:
1-4. Work backwards. Use the chart if you have to, but these should be memorized by now.
5-6. Calculator. Functions are ‘above’ sin and cos buttons.
11-12. Same as #5-6 but put in DEG mode.
13. Picture the y = Arccos x graph. What will 3x do to the x –values? What will +1 do to the y-values?
15. Be careful here. The back of the book is wrong in some of your texts! The answer is 0.33pi.
16-17. First quadrant—REAL EASY!
20. Look at the graph of y = Arccsin x (we did it in class). What happens when you add 1?
24. Think? How else could we “chop-up” the sine function to make it one-to-one?
29. Do the inside first.
30-31. Like Granny says, draw a reference triangle!
35. Set equal to zero, graph, and locate the zero.
43-44. Factor like a quadratic and use the zero product property. check 4.5 hwk
Wednesday 11/21: Quiz
Monday 11/19-Tuesday 11/20: 4.7 Simple Harmonic Motion: worksheet 2 (solutions to both). Did you hand in Trig Function Scavenger Hunt? Did you finish 2.1 Problem Set (quia)? Did you finish Section 4-7: Practice Exercises pp233-235 #1-9 (odds), 13-14, 17, 22, 25, 27, 30, 32, 33, 35 ? Quiz Wed.
Friday 11/16: 4.7 Simple Harmonic Motion: worksheet 1 (solutions to both)
Homework (due Wed)-- Section 4-7: Practice Exercises pp233-235 #1-9 (odds), 13-14, 17, 22, 25, 27, 30, 32, 33, 35.
1-9 (odds). General sinusoid: y = a sin b(x-c) + d
amplitude = a, period = 2pi/b, frequency = 1/period.
The unit for the period is seconds/cycle, the unit for frequency is cycles/second or Hz.
13. a = 2.5, pd = 4pi/3 (hard to tell from graph)
14. pd = 3pi/2 (hard to tell from graph)
17. This should be a –cos function.
22. pd = 12.25 hrs.
25. pd = 2 sec
27. f = ¼ Hz
30. did in class.
32. f = 5 Hz, a = 40
33. d = 4 (sinusoidal axis), a = .35, pd = 5.4
35. a = 10, pd = 0.9, (0, -5) is a point on graph. Tricky, because it has a phase shift.
check 4.7 hwk solutions
Thursday 11/15: Finish Trig Function Scavenger Hunt. Hints below.
Assign: 2.1 Problem Set (quia)-- you'll have some time in class on Thursday for this (must be finished by Saturday at noon).
Wednesday 11/14: Trig Function Scavenger Hunt -- group assignment (3-4 people per group, 1 paper handed in per group)
Hints: y = a sin b(x - c) + d
period = 2pi/b for sine, cosine, secant, and cosecant.
period = pi/b for tangent and cotangent.
Specific problems:
1. pd = 2pi/3;
2. pd = 4pi
3. Sine is shifted pi/4 right, cosine 3pi/4 right.
4. d = 1
5. d =-1/2
6. a = 3/2
7. a = 2 . Secant function
8. Tangent shifted pi/4 right
9. Cotangent shifted down 1
10. pd = pi/3.
11. pd = pi
12. d = -1, a = 2
Assign: 2.1 Problem Set (quia)-- you'll have some time in class on Thursday for this (must be finished by Saturday at noon).
Quiz Tuesday
Tuesday 11/13: 4.3 Tangent and Secant Graphs (solutions) If you're stuck watch a video: graphing cosecant; other trig functions.
Monday 11/12: 4.3 Tangent Graphs (solutions)
Assign: 4.3 Practice Exercises pp206-207 #17,19, 21-24, 26-27, 35, 37, 39, 44. (due Wed)
17, 19. Just get the asymptotes using the method developed in class. The phase shift will take care of itself.
21-24. Remember that tan and cot give horizontal points of inflection, and sec and csc give “caps” and “cups”.
26. This is tangent but the period changed. For tangent, period = pi/b
27. This is cosecant but it was shifted down and the period changed.
35, 37, 39. Just get the asymptotes using the method developed in class. The phase shift will take care of itself. Remember that tan and cot give horizontal points of inflection, and sec and csc give “caps” and “cups”.
44. amplitude = ½(600) = 300, period = 12.5 = 2pi/b.
check 4.3 homework: part 1, part 2
Friday 11/9: AT-PAC #1
Thursday 11/8: Quarterfinal (calculator allowed)
Wednesday 11/7: Quarterfinal (no calculator)
Monday 11/5: Quarterfinal Review (solutions). The quarterfinal is Wed 11/7 (no calculator) and Thurs 11/8 (calculator allowed). This review packet is similar, but not identical, to the actual test. You should also study class notes, previous quizzes, and know the unit circle and trig identities. In order to study, you can all skip school on Tues 11/6. You're welcome.
Friday 11/2: Escape Room Activity
Thursday 11/1: Finding Sinusoidal Equations (solutions)
Assign: 4.2 Practice Exercises pp196-199 #1-4, 7-8, 11, 13, 16-17, 19, 21-23, 27-29, 40-44, 49-50. (due Fri. Hints below)
Wednesday 10/31: 4.2 Period, Amplitude, Phase Shift, and Sinusoidal Axis (solutions)
Assign: 4.2 Practice Exercises pp196-199 #1-4, 7-8, 11, 13, 16-17, 19, 21-23, 27-29, 40-44, 49-50. (due Fri)
1-2. Amplitude is from the middle (sinusoidal axis) to the top (or bottom). Alternatively, you can measure from top to bottom and divide by 2.
3-4. Amplitude is always positive.
7-8. period = 2pi/b. For #8, sin (-12 θ) = -sin (12 θ), since sine is an odd function.
11, 13. For y = a sin bx, a is the amplitude and 2pi/b is the period. #13 will have ugly answers.
16-17. There are many possible answers for these.
19, 21-23. Just find the equation in the form y = a sin b(x-c) + d, For #22 use cosine (it starts at a high point).
27. Don’t forget to factor out b: y = 4 cos2(x + pi) + 2
29. Don’t forget to factor out b: y = 0.1 cos3(x - 2pi/3)
40. period is 2pi, sine is shifted pi/4 right
41. period is 2pi/3, sine is reflected in the x-axis
42. period is 2, make it a cosine.
43-44. A couple of real-word applications of this stuff. frequency = 1/period (the reciprocal of the period)
49. Draw a picture. The spring oscillates between -16 and +16. (i.e. 16 is the amplitude). ¼ cycle per second is the frequency, which means the period is 4. Use period = 2pi/b to get b. “pulled down 16 cm and then released” tells you to use a negative cosine function.
50. “displacement of a pendulum clock is 10 in.” means the amplitude is 10. “one complete cycle in 4 sec” means the period = 4. The problem doesn’t mention a starting point so a sine or cosine is fine here.
check 4.2 hwk solutions: part 1, part 2
Tuesday 10/30: 4.1-4.2 Sinusoids (solutions)
***You have Monday night hwk due Wed.
Monday 10/29: 4.1 Graphs of Sine and Cosine (solutions)
Periodic functions: The y-values repeat-- f(x + h) = f(x). h is called the period. The period for sine and cosine is 2pi.
Assign: Practice Exercises pp187-188 #1, 3, 5, 9, 13, 15, 20-23, 26, 30, 38, 39, 40. (due Wed) Very important to use you calculator to check your work only—don’t use it as a crutch!
1,3. If it’s periodic f(x+h)=f(x) for a value h. h is called the period. In other words, do y values repeat regularly? If so, how far do you have to travel (left to right) before you start repeating yourself?
5, 9, 13. These just change the amplitude and sinusoidal axis. Remember a negative in front of the function is a reflection in the x-axis.
15. A cycle is an interval of a full period, usually (0, 2pi). As an example y = sin x is increasing on (-pi/2, pi/2) and decreasing on ( pi/2, 3pi/2).
20-23. Use the cofunction identity (p186)
26. Easy, use the amplitude and vertical shift.
30. Graph these using the methods described in class using amplitude, period, phase shift, and sinusoidal axis.
38-39. Easy, use the amplitude and vertical shift.
40. For even functions f(-x)=f(x). Check 4.1 solutions: part1, part 2.
Friday 10/26: Problem Set #5-- Trig Identities (quia). Sorry, quiz is online.
Thursday 10/25: Review hwk answers: 3.8 hwk solutions; 3.9 hwk: part 1, part 2
Review Problem Set (solutions) Quiz Fri. Quarterfinal 11/7 and 11/8.
Wednesday 10/24: Kahoot! Then finish pp174-175 #1-2, 4, 5, 6, 8, 10, 11, 15, 17, 19, 21, 24, 35. (p8 of the pdf; due Thurs), quiz Fri.
Tuesday 10/23: 3.9 Proving Trig Identities (solutions)
section 3-9: pp174-175 #1-2, 4, 5, 6, 8, 10, 11, 15, 17, 19, 21, 24, 35. (p8 of the pdf; due Thurs) Some of these are tough. They take lots of space and even more concentration—don’t give up easily on these. You can do it!!!!!
1-2. Change to sines and cosines.
4. Get a common denominator of cos θ(1 + sin θ). Do not multiply out the denominator (you’ll want to cancel later!). The numerator becomes 1 + 2sin θ + sin²θ + cos²θ. Since sin²θ + cos²θ = 1 , we get 2 + 2sin θ. Now factor out the 2 and cancel.
5. Multiply out left side and use Pythagoream Identity.
6. Factor the left side as difference of squares.
8. Easy—Pythagorean Identity.
10. Start with the right side and split the fraction.
11. You shouldn’t need a calculator for this one!
15. Change to sines and cosines.
17. Factor out 100 and use Pythagorean Identity.
19. 1 - sin²θ = cos²θ
21. Get a common denominator of (1 - sin θ) (1 + sin θ).
24. Pick 2 angles to show that this equation does not work in general.
35. Factor the left side as a difference of squares and use Pythagorean Identities.
Monday 10/22: Finish Trig Identities Worksheet (solns)
Homework: section 3-8: pp169 –170 #22, 26, 31-37, 44-45. These start on p6 of the pdf
Homework help:
22. Use Pythagorean Identities:
1 + tan²θ = sec²θ
1 + cot²θ = csc²θ
26. sin²θ + cos²θ = 1, now divide everything by sin²θ.
31-33. Use ratio identities and reciprocal identities
34. Use 1 + cot²θ = csc²θ
35. Use 1 + tan²θ = sec²θ
36. Use sin²θ + cos²θ = 1
37. Get a common denominator and use sin²θ + cos²θ = 1.
44. 1 - sin²θ = cos²θ
45. tan θ = sin θ/cos θ and cross multiply.
Friday 10/19: 3.8 Fundamental Trig Identities (solns); Trig Identities Worksheet (solns); extra: Lots of Practice
video: simplifying trig identities
Thursday 10/18: 3.7 Problems (check solutions), finish homework (below), work on quiz corrections, if necessary. Quiz 3 retake due by Thurs 10/27.
Wednesday 10/17: 3.7 Evaluating Trig Functions (solutions)
Assign: pp163-164 #1-19odds, 23-28, 39, 41, 49. (due Fri)
Help section 3-7:
Make sure your calculator is in the correct mode: DEGREE or RADIAN
1. too easy
3. sin(127+5/60+10/3600)
5. 1/cos18
7. see #5
9. see #3
11. too easy
13. no calculator on these!
15. work backwards, use cos-1(-0.5023). Find the answers in QII and QIII.
17. work backwards, use sin-1(0.8143). Find the answers in QI and QII.
19. work backwards, use tan-1(-0.2677). Find the answers in QII and QIV.
23. Gettin’ tougher here. sec theta = 1.1111 is equivalent to cos theta = 1/1.1111. Now work backwards, use cos-1(1/1.1111). Find the answers in QIII and QIV.
24-28. Similar to #23. Get the reciprocal to put in terms of sine, cosine, or tangent, and then work backwards. Pick the appropriate quadrants.
39. This factors like a trinomial: ( )( )=0. Then use the zero product property.
41. This is just a “real-world” application of this stuff. Just plug-in to the formula and solve for g.
49. The easiest way to do this is to put the function into y1 , graph it, and use the Calc-value feature of your calculator. Check 3.7 solutions: part1, part2
Tuesday 10/16: Quiz
Monday 10/15: Review Problems (check solutions), quiz Tuesday (no calculator-- mainly unit circle questions).
Friday 10/12: Collins's classes: Problem Set #4 (quia) . Creighton's classes: Problem Set #4 (quia)
Thursday 10/11: 3.6 Trig Practice (solutions) check 3.6 solutions part 1, part 2.
Wednesday 10/10: PSATs (crazy schedule). Finish 3.6 assignment (below)
Tuesday 10/9: 3.6 Functions of Special Angles: working backwards (solutions)
Assign: Section 3-6: pp157-158 #3-6, 9, 11, 13, 15, 17. pp157-158 #24-34, 43, 45. start on page 7 of the pdf. (due Thurs)
3-6. The reference angle is the angle made with the x-axis. It is always an acute angle less than pi/2 ( or 90 degrees). Make sure to draw the angle in standard position.
9. Draw the reference triangle.
11, 13, 15, 17. Draw the reference triangle. Find the reference angle and use those trig values. Use ASTC to get signs.
24-34. Use your Collins Chart and ASTC.
43, 45. Again, use the Collins Chart
Friday 10/5: Finish 3.6 Functions of Special and Quadrantal Angles; then Problem Set 1.3. Trig Flashcards
Thursday 10/4: 3.6 Functions of Special and Quadrantal Angles (solns)
Wednesday 10/3: Finish last page of 3.5 The Trigonometric Functions (solns), start 3.6 Special Angles (solns)
Monday 10/1: 3.5 The Trigonometric Functions (solns). Did you finish Linear and Angular Velocity Practice (solutions)? Quiz Tuesday.
Friday 9/28: 3.4 Circular Functions (Solns)
Unit Circle-- Circle with a radius of 1 centered at the origin.
sinθ = y-coordinate on the unit circle
cos θ = x-coordinate on the unit circle
Homework: pp145-146 Practice Exercises #1-12, 18-36 (evens), 43. (1st 2 pages of pdf) (due Wednesday)
Hwk Help Section 3-4:
1. These are quadrantal angles (they terminate on either the x- or y-axes). The answers should be -1, 0, or 1.
2. 225 deg is a 45 degree angle in the 3rd quadrant. Use your knowledge of 45-45-90 right triangles. (The sides are 1-1-sqrt2). 810 degrees = 720 + 90 so it is coterminal with 90 degrees.
4-9. Sine (y) is positive in QI and QII but negative in QIII and QIV. Cosine (x) is positive in QI and QIV, but negative in QII and QIII.
10-12. see Ex3, p143.
18. Draw a reference triangle and use the Pythagorean Theorem to find y. Then use the definitions of sine and cosine.
20. Cosine of anything is always less than or equal to 1 (it’s the x-coordinate on the unit circle).
22. Again, use the unit circle.
24. Express 0.8 as 4/5 and draw a reference triangle.
26-32ev. Use your unit circle and the fact that sine is positive in Quadrants I and II and negative in QIII and QIV. Why? Also, cosine is positive in QI and QIV and negative in QII and QIII.
34. On the unit circle, if x = 1, then what does y equal?
36. On the unit circle, if x = 0, then what are the 2 possible values for y?
43. There’s only 3 values for sine that you know right now—0, -1, and 1. These are the answers. check solutions: part 1, part 2
Thursday 9/27: Quizzizz activity; Linear and Angular Velocity Practice (solutions). If you did the remediation assignment you can check your answers here.
Wednesday 9/26: work session. Quiz Tuesday
Assign: Section 3-3 (part 2): pp137-140 Practice Exercises #25, 27, 31, 33, 35, 41, 43, 45. (skip to p9 of the pdf) (due Thurs)
Hints:
25. These are both angular velocities. Use dimensional analysis to get the units correct.
27. Convert degrees to radians and use V = r*theta/t. Make sure to get the units correct.
31. Convert diameter to radius (divide by 2). Convert revolutions to radians, then use V =rw.
check hwk solutions (part 2)
Tuesday 9/25: 3.3 Linear and Angular Velocity (solutions)
Assignment: Section 3-3 (part 1): pp137-140 Practice Exercises #1, 5, 6, 9, 10, 13, 15, 19, 21. (skip to p9 of the pdf and do the PRACTICE EXERCISES) (due Thurs)
1. 1 rev = 2pi radians
5-6. Use 1 rev = 2pi radians and 1 min = 60 sec
9-10. Use 1 rev = 2pi radians and 1 min = 60 sec
13-15. Use V =rw. Make sure to get the units correct.
19-21. Convert degrees to radians and use V = r*theta/t. Make sure to get the units correct.
check solutions (part 1)
Monday 9/24: Quia Problem Set #2, opportunity to retake quiz, ask questions, etc.
Friday 9/21: Angles and their measures practice (solutions); arc length and sector area (solutions)
Thursday 9/20: 3.1 Angles and Their Measures . Assign: Finish back of sheet (solutions)
Retakes: You have until Friday 9/28 to retake the first quiz. You must fix your mistakes on the original quiz first and complete a quiz remediation assignment. You can always stop in to see Mr. Collins or Mrs. Thompson for help. (You can ask either teacher, we both teach the same course). There are videos you can watch (listed below) and deltamath activities (domain/range) that you can practice with. You may retake the quiz before or after school in E-110 (make sure you give yourself enough time to take the quiz). You get the higher grade, so make sure you know your stuff before you attempt the retake. check remediation solutions.
Tuesday 9/18: Quiz
Monday 9/17: Unit One Review Problems (solutions)
video help: Graphing a piecewise, Graphing with transformations; How to find the domain of any function
Friday 9/14: Practice problems for Tuesday's Quiz.
Thursday 9/13:
For Collins's classes: Finish Delta Math assignments for Domain & Range and Transformations. I'm here to help with technical problems. QUIZ Tuesday.
For Thompson's classes: Transformations article.
Wednesday 9/12: Graphs and Transformations
some videos that might help: Graphing with transformations; How to find the domain of any function
First Quiz Tuesday
Tuesday 9/11: 1.4 Domain and Range (solutions) Some tips to help you determine the domain:
1. Vertical asymptotes occur at x-values that make the denominator equal zero (You cannot divide by zero!).
2. The number under the square root cannot be negative.
Homework: Try Delta Math assignment.
For Collins's classes: deltamath.com -- Create a student account.
Teacher Code: 378779; pick your appropriate period.
Friday 9/7: Exploration of Functions Day 2. More practice from yesterday. Wrap up of Exploration of Functions / Notes on Functions
class: #5, 11, 16 (solns)
*Homework: Algebra 2 and Geometry Review (quia)
Use Desmos Online Graphing Calculator as necessary.
Thursday 9/6: Function Notes (solution), extra help videos: increasing and decreasing intervals, domain and range of a graph.
Assign (due Friday): Exploration of Functions Day 1. (#2, 4, 6, 8) We want to see what you know about functions. Some vocab that you should be familiar with by the end of the week: function, relation, domain, range, increasing/decreasing, end behavior, continuity, symmetry, transformations, odd/even functions, zeros, intercepts, asymptotes, one-to-one. solutions.
Due Tuesday: Algebra 2 and Geometry Review (quia) To sign up for Quia see instructions below.
Wednesday 9/5: Finish Function matching activity.
Review Course expectations: Mrs. Thompson's Course Expectations Mr. Collins's Course Expectations
Sign up for Quia
Step 1. Go to the Quia website at https://www.quia.com/web.
Step 2. Now, click the area labeled Students. When the next page appears, enter your username and password if you already have a Quia account. If you do not have an account, click the link Create my free account. Fill out the form that appears. Select "Student" as the account type. When you are done, press the Create my account button.
Step 3. You should now be in the Student Zone. Type in the class code (see below) in the text field and press the Add class button. Now you're done!
Quia Codes:
Collins- Honors PreCalc 1 KFJC866
Collins- Honors PreCalc Period 7/8 PKPXH948
Collins- Honors PreCalc Period 9 KHBCMJ477
Thompson- Honors PreCalc Period 10 MJGCJ773
Thompson- Honors PreCalc Period 2 BGHXR499
Thompson- Honors PreCalc Period 4/5 GNEAK384
Now that you have registered for your instructor's course, you can view your class web page, take quizzes, view your quiz results, view time spent on Quia activities, and read your instructor's feedback from your Quia account.
Follow these steps to view your results:
Step 1. Log in to your account. (Remember, go to the Quia Web home page at https://www.quia.com/web and click the area labeled Students.)
Step 2. Click on the class name
DueTuesday: Algebra 2 and Geometry Review (quia)
Tuesday, 9/4: Welcome Back. Precalculus is the study of functions. We're going to start right in and look at some functions.
Function matching activity-- We'll look at everyday situations and try to match them up with functions (in the form of a graph and an equation).
Mrs. Thompson's Course Expectations
Mr. Collins's Course Expectations
2017-2018
Keynote study slides: #1, #2, #3, #4, #5, #6
UM Cycle Days Life advice: Don't be this guy!
Wednesday 5/30-Thursday 5/31: Limits and Derivative Review TEST FRIDAY
Tuesday 5/29: Binomial Theorem example video
TEST FRIDAY (Review Wed and Thurs; you may retake quizzes Thurs in class)
Wednesday 5/23: 16.5 Review Problems (solutions) ***note the typo in #5-- numerator should have a 2. QUIZ THURSDAY
Monday 5/21-Tuesday 5/22: (Keystone Testing) 16.5 "The Big Shortcut"--this is for polynomials (not every function) (solutions) QUIZ THURSDAY
Thursday 5/17-Friday 5/18: (Keystone Testing) 16.4c The Derivative
Wednesday 5/16: 16.4b The Derivative (solutions)
Monday 5/14-Tuesday 5/15: (Keystone Testing) 16.4 The Derivative (solutions)
Assign 16.4: pp874-875 #3-4, 11, 15, 17, 20, 29-30, 35, 40. (pp4-5 of pdf, we'll do a lot of these in class, due Monday)
3-4, 11. limit as h approaches 0 of [f(x + h) – f(x)]/h. The second derivative is the derivative of the first derivative.
15, 17. Get rid of complex fractions by multiplying top and bottom by LCD.
20. congugate
29. 24, The function is not differentiable at 24 (there’s no left hand limit there).
30. The function is differentiable at all points on the domain.
35. Find the derivative and set it equal to -4.
40. Same thing as usual—get the h’s to cancel out.
Thursday 5/10: Thompson: Quia Problem Set (Tangent Lines); Collins: 4.3 Quia Problem Set (Tangent Lines)
Wednesday 5/9: Problem Set
Tuesday 5/8: Warm-Up: Cape May Trip
More tangents to a curve (answers)
Monday 5/7: 16.3 Tangent to a Curve
Assign: (16.3) pp869-870 #3, 4, 8-10. (due Wednesday)
For all of these use the difference quotient:
limit as x approaches c of [f(x) – f(c)]/(x – c).
(c, f(c)) is the ordered pair given in the problem.
All of these limits are indeterminate forms, “0/0”, which can easily be handled by factoring.
Thursday 5/3: Problem Set (check solutions)
Wednesday 5/2: Collins: 4.2 Problem Set (quia); Thompson: Limits Review (quia) QUIZ FRI
Tuesday 5/1: Limits packet. Evens on last page for hwk.
Monday 4/30: check answers to 16.1 hwk. The even solutions are here. Desmos limit activity. Assign: #1-5 of packet
Thursday 4/26: 16.2 Limit Theorems
Wednesday 4/25: 16.1 Limit of a Function
Assign: (sect 16.1) pp857-858 #1-14, 17-30, 33-36, 41-44. (due Fri)
#1-6. These are actually 4 part questions: a) left hand limit as x approaches c, b) right hand limit as x approaches c, c) limit at c, d) f(c).
REMEMBER—LIMITS ARE y-values!!!!!
7-10. Again, limits are y-values.
11-14. “plug-in”
17-25. These are all continuous functions; remember that polynomials are continuous everywhere. So, just plug-in the values. Yes, it’s that easy!
26. The bottom of a fraction gets really big.
27-28. Polynomials = continuous = plug-in.
29. Use the top part of the function and factor.
30. Plug into both sides of the function.
33-36. Graph
41-44. Plug-in.
Friday 4/20: Exponential Growth/Decay Activity (with M&Ms!); Last ATPAC Monday; TEST Tuesday
Thursday 4/19: 4.1 Problem Set (quia); check 9.6 hwk answers
Wednesday 4/18: ch9 Review Problems; Last ATPAC Monday; TEST Tuesday
Hints:
1. base > 1 growth (increase); base < 1 decay (decrease). Exponents have HA, logs have VA.
2. base > 1 growth (increase); base < 1 decay (decrease). Exponents have HA, logs have VA.
3. da, da, da, ….. logb x = y means by = x
4. Get the VA and go from there.
5. 3 second problem.
6. 2 second problem.
7. 12 second problem.
8. log both sides (or ln both sides if you care about the environment)
9. da, da, da, ….. logb x = y means by = x
10. logb x = (log x)/(log b)
check solutions to review problems.
Tuesday 4/17: 9.6 Modeling with Exponentials and Logs
Hwk: (sect 9.6) pp478-479 Practice Exercises #5-6, 8-10, 23-25. (due Thurs) A good thing to keep in mind in all of these problems is that the subscript 0 means the amount at time = 0 or the original amount. For example P0 would mean original population.
Hints:
5-6, 8. Plug in what you’re given, ln x “undoes” ex.
9. Use the formula A = A0(2)-t/5570. (see p 477, Example 3)
10. Plug in what you’re given, ln x “undoes” ex.
23. A good idea here is to let 1981 be year t = 0, so 1983 would be year t = 2. P0 = 23,153.
24. Let N = 70 and solve.
25. In calculator: y1 = 5e^(-0.4x); y2 = 2.25. Find the x where these two graphs intersect. (get a good window). Then do the same with y1 = 5e^(-0.4x) and y3 = 0.5
Monday 4/16: 9.6 Natural Logarithms (solutions); finish what's not done in class for hwk. videos: solving with ln and e; properties of logs.
Friday 4/13: Review 9.4 hwk solutions; quiz
Thursday 4/12: 9.1-9.4 Problems (check solutions); quiz Friday; finish 9.4 Hwk.
Wednesday 4/11: 9.4 Properties of Logarithms (solns) ; check 9.3 HWK
Assign: (due Fri) sect 9.4 pp464-466 #21-26, 31-35, 37-38.
21-24. Use log properties.
25. Remember that ln e = 1 and ln en = n
26. log 10n = n
31-33. Again, use the log properties to get a single logarithm and then use “da, da, da,…” to change it to an exponential equation.
34. Plug in. You’re solving for P.
35. Plug in.
37. Use the change of base formula: logb x=(log x)/(log b) and also use the fact that log 10n = n. Remember that 0.1 = 10-1.
38. Use the change of base formula: logb x=(log x)/(log b) and also use the fact that log 10n = n. Remember that 100 = 102. check 9.4 hwk
Tuesday 4/10: 9.2 Interest Formulas Quiz Friday
Hwk due tomorrow (see below)
Monday 4/9: Polygraph Activity: Exponential & Logarithmic Functions
Assign: (due Wed) PRACTICE EXERCISES sect 9.3 p458 #5-9, 15, 18, 28, 32, 40-43, 45 (starts on p2 of pdf)
5-7. Change logs to exponents using “da, da, da, ….”
8. e is the base of the natural logarithm.
9. You’re graphing 3y=x
15. too easy
18. logb x=(log x)/(log b)
28. graph ‘em. what do you notice?
32. plug in
40-43. These are a little tough, but you can do them. The general equation is y = logb(x – c)+d where c is the vertical asymptote. You can fill in the other ordered pairs to find b and d.
45. You can actually just plug in.
Friday 4/6: Graphing Logarithms
Thursday 4/5: 9.2 More Exploration of Exponential Models
Wednesday 4/4: 3.5 Problem Set (quia)
You may want to brush up on your rules for exponents since some of these questions include some review problems from algebra: video #1, video #2, video #3.
Tuesday 4/3: Exponential Functions Exploration-- today we look at e, an important mathematical constant.
e ~ 2.718281828459045......
Here's a good website about exponential growth and decay.
Monday 4/2: Exponential Functions Exploration; finish handout for hwk.
Tuesday 3/20: AT-PAC #5
Monday 3/19: Review test answers; finish any outstanding quias.
Thursday 3/15: check Review Solutions
Wednesday 3/14: 3.4 Problem Set (quia)
Tuesday 3/13: 7.7 Radical Functions (solutions) Test this Friday. Assign: Review Sheet #2, 4, 7, 10, 14, 19, plus last night's if not done.
Monday 3/12: 7.7 Radical Functions (solutions) Test this Friday.
Assign: #4, 6 from 7.7 Radical Functions and #1, 3, 9, 12, 16-18 on Review Sheet
Friday 3/9: Function Scavenger Hunt Graded out of 10 points, 12 points possible. Just find a function that fits the given criteria. Test next Friday.
Hints for Scavenger Hunt:
1. A rational function; you can leave it in factored form.
2. Too easy.
3. Trig function.
4. A rational function; you can leave it in factored form.
5. You've got this!
6. y = 1/x has a horizontal asymptote at y = 0.
7. A square root function. Just move it!
8. Use the sum and product of the zeros theorem (Kush's Thm).
9. A parabola?
10. A step function?
11. Make up a piecewise function.
12. The exponential function, y = 2^x has a R = (0, inf), just move it up 1.
Bonus: A trig function.
Thursday 3/8: check 7.6 hwk; Finish back of How do find asymptotes?
Tuesday 3/6: How do find asymptotes?
Monday 3/5: 7.6 Rational Functions (solutions)
videos: How to find horizontal asymptotes. How to find vertical asymptotes.
Assign: Practice Exercises (sect 7.6) pp368-370 #8, 10, 12, 36, 39, 45. (due Wed)
8. It’s the greatest integer function—MATH-NUM-INT (on TI-84). At what x-values do you “jump”?
10. It’s a piecewise function. Make sure to check x = 4.
12. What happens at x = 5?
36. What happens at x = 3. Find intercepts—y-int (set x = 0), x-int (set numerator = 0). Horizontal asymptote? Compare the degrees of numerator and denominator—if tied, divide the leading coefficients.
39. What happens at x = -1, and x = 6. Find intercepts—y-int (set x = 0), x-int (set numerator = 0). Compare the degrees of numerator and denominator.
45. Horizontal asymptote? Compare the degrees of numerator and denominator—if tied, divide the leading coefficients. Vertical asymptote—zeros out the denominator, but not the numerator
Thursday 3/1: Review Problems (solns)
Wednesday 2/28: Review AT-PAC answers. Finish 7.4 Fundamental Theorem of Algebra (solutions) Quiz Fri
Tuesday 2/27: 7.4 Fundamental Theorem of Algebra (solutions) Quiz Fri
An nth degree polynomial will have n rational zeros.
Kush's Thm: For a quadratic ax^2 + bx + c, the sum of the zeros is -(b/a) and the product of the zeros is c/a.
Assign: Practice Exercises (sect 7.4) pp353-355 #24, 26, 28, 34 (use calc), 37-38, 46. (due Thurs)
24, 26, 28. Remember that Complex Roots and Radical Roots come in conjugate pairs. (i.e. If -1- i is a root, then -1 + i is a root.)
34. Use your calculator to find the lowest point of the graph between x = 0 and x = 6. Adjust your window so you can see the whole graph.
37, 38. Use the theorem (Kush’s Thm) about the sum of the zeros and the product of the zeros of a quadratic.
46. Set equal to zero and solve. check 7.4 HWK
Monday 2/26: ATPAC #4
Thursday 2/22-Friday 2/23: Finish 7.3 hwk (see below); 3.3 Problem Set (quia)
Wednesday 2/21: 7.3 Rational Zeros Theorem (solutions)
BONUS ANSWERS on handout: #1. 3 + sqrt6, (5 + 3sqrt3)/2, (5 - 3sqrt3)/2. #2. pi/6, 5pi/6, 7pi/6, 11pi/6, 3pi/2
Assign (due Mon): Practice Exercises (sect 7.3) pp347-348 #22, 24, 26, 27, 34, 36, 38, 40, **43—5 solutions to this one! **bonus
Hints: 22, 24, 26. Synthetic division. Guess and check until you get a remainder of zero. Get down to a quadratic so you can factor.
27. Draw a good picture. Then write an equation for volume.
34. Same stuff. Synthetic division.
36, 38. Graph it if you get stuck finding a zero.
40. Similar to what we did in the last section: 3 is your multiplier and -1 is the remainder.
43. Replace cos2x with 1 – sin2x. check 7.3 solns
Tuesday 2/20: 7.2 Warm-up and Notes; 7.2 Graphing Polynomials
Good stuff to know about polynomials: Webpage that may help
1. Polynomials are smooth CONTINUOUS curves. The domain is all reals.
2. nth degree polynomials can have up to n real zeros. They have exactly n zeros if we include complex zeros and multiplicities.
3. nth degree polynomials can have up to n - 1 extrema. Extrema are max and min points.
4. A horizontal inflection point is not an extrema.
5. Even degree polynomials have the shape of a "touchdown"; odd degree polynomials are shaped like "stayin' alive."
6. Zeros are also known as roots. These are x-intercepts for real zeros.
7. Extrema are minimum and maximum points. We usually call these relative minimums and relative maximums.
8. End behavior: Even degree functions start high left and end high right (like y = x^2, a parabola). Of course a negative in front changes the shape to an upside down parabola, so it would start low left and end low right. Odd degree functions start low left and end high right (like y =x^3, the basic cubic function). And again, a negative in front would flip the graph in the x-axis.
Assign: Practice Exercises (sect 7.2) pp340-342 #10, 12, 18-20, 22, 25-29, 35, 37, 45. pages 3-4 of pdf (due Wed)
Hints to homework assignment:
10, 12. Just a “rough sketch” of the graph. The multiplicity determines how the graph “cuts though” the x-axis.
18-19. Remember, Even: f(-x) = f(x), symmetric in y-axis; Odd: f(-x) = -f(x), symmetric in the origin. NOTE: This is not the same as even and odd degree.
20. How many extrema does y = x4 have?
22. Draw it.
25-26. Work backwards. Leave your answer in factored form.
27-29. No problem. You’ve got this.
35, 37. This is a way to use the graph to factor a polynomial.
45. Good Luck! check 7.2 hwk solutions
Wednesday 2/14: 3.2 Problem Set (quia)
Tuesday 2/13: check homework answers. Synthetic Division and the Remainder and Factor Theorems
Stuck? Use the hints below.
Hints:
1. 2 is the multiplier and -5 is the remainder; do synthetic substitution and don't forget the cubic term.
2. -1 is the multiplier and 0 is the remainder; do synthetic division.
3. Do synthetic division twice with 1 and -1 as the multipliers and then set the remainders equal to solve for k.
4. 5 is the multiplier and 0 is the remainder; do synthetic division.
5. Do synthetic division twice.
6. Find A first.
7. Try 1 as a multiplier. Then you can factor the quadratic.
Monday 2/12: Dividing Polynomials (check solutions); practice problems
Thursday 2/8-Friday 2/9: Test
Tuesday 2/6: Chapter 6 Review (check solutions)
Friday 2/2: Chapter 6 Review (check solutions)
Thursday 2/1: check-in quiz; Test Tuesday.
Wednesday 1/31: 6.5 Practice Problems (Check answers); Collins: 3.1 Quia; check-in quiz tomorrow.
Tuesday 1/30: Quizlet HWK: Thompson #9, 20, 22; Collins #16-20.
Monday 1/29: 6.5 Solving Trig Equations (solutions) need help? video
Solutions to #1-15 and #16-30. HWK: Complete up to #15 Mon Night
Friday 1/26: 6.5 Solving Trig Equations (solutions) Complete #1-5 for HWK.
Solutions to #1-15 and #16-30.
Thursday 1/25: Review AT-PAC; review last quiz
Wednesday 1/24: AT-PAC #3
Monday 1/22: Review Quia-- non-calculator Quiz Tuesday (modeled after Friday's Review Problems (solutions) Any questions? See Mrs. Thompson in E110.
Friday 1/19: Review Problems (solutions) Quiz Tuesday (no calc)
Thursday 1/18: Product/Sum Identities (solutions)
Wednesday 1/17: extra practice (solutions)
Double Angle identities are for problems of the form sin(2α), cos(2α), tan(2α).
Half Angle identities are for problems of the form sin(α/2), cos(α/2), tan(α/2).
Tuesday 1/16: 6.3 Double and Half-Angle Identities (solutions)
Thursday 1/11- Friday 1/12: 6.1 Sum and Difference Identities (solutions)
Collins HWK #2, 6, 8, Thompson HWK #3, 4, 8.
Now we look at problems of the form sin(α + β). Guess what? It's not sin α + sin β. In fact, sin(α + β) = sinα cosβ + cosα sinβ. This allows us to find the trig values of angles like 15º, 75º, π/12, 7π/12, etc.
website (with proofs & examples); video of sin 195°
Test Wednesday 1/10
Extra Review: ch5 Test (text, 4th page of pdf), check solutions)
Monday 1/8- Tuesday 1/9: check hwk; Review Problems (check solns)
Wednesday 1/3: We'll try a few more examples in class and finish assignment from Tuesday. (see problems and hints below)
Tuesday 1/2: 5.5 Areas of Triangles (and other shapes) (check solutions)-- You thought you knew how to get the area of a triangle? Yeah, right: as in you needed a right triangle. Guess what? We can calculate the areas of non-right triangles. I don't know why we wait until now to tell you about this.
If we know all 3 sides (SSS) we can use Heron's Formula to get the area of a triangle. If we have SAS you can use this method (no cool name for this one).
Homework: pp276-279 (sect 5.5) Practice Exercises #11, 12, 17, 20, 22, 27, 29, 30; #31, 35, 39, 41, 49, 51, 53. (due Thurs) ch5 Test Tuesday
Hints:
11. Area of a segment = Area of a sector – Area of triangle. Area of a sector = ½ r2 θ, when θ is in RAD
12. Area of a sector = (θ/360)pi*r2, when θ is in DEG.
17. Use Heron’s Formula to find the area, then use A = ½ bh and use t as the base to find the altitude to RS.
20. Use Heron’s Formula.
22. Divide into triangles and use ½ absinC.
27. Use ½ absinC backwards.
29. Connect B to D and find the area of each triangle.
30. Divide hexagon into 6 congruent (and equilateral) triangles.
31. Divide pentagon into 5 congruent triangles and use ½ absinC.
35. Area of a sector = (θ/360)pi*r2, when θ is in DEG.
39. Triangle – ½ circle. Each of those sectors is a 1/6 of a circle.
41. 6-8-10 right triangle.
49. Draw the radius from the center to a corner point of one of the crosses.
51. Find the square – the quarter of a circle.
53. Use a 30-60-90 triangle to find the radius.
Quiz Thursday
Wednesday 12/20: answers to odd problems from last night; Applications of triangle trig (check solutions)
Tuesday 12/19: The Law of Cosines (check answers) Assign: #1, 3, 5, 7, 9.
Monday 12/18: The Ambiguous Case
Friday 12/15: Quia Problem Set: Collins's classes
Thursday 12/14: Law of Sines
Homework: pp254-256 (sect 5.2) #3, 6, 9, 15, 22, 24, 27, 30, 41, 43. start on p6 of the pdf. (due Mon)
3, 6, 9. Use sinA/a = sin B/b = sinC/c
15. Draw a good picture.
22. AAA?
24. Find the 3rd angle first.
27. Again, start with a good diagram.
30. Fill in all angles first.
41. Tricky—don’t find theta! Try to get the other angle first!!!!!
43. Work with 1 triangle at a time.
45. Work with 1 triangle at a time.
Wednesday 12/13: ATPAC #2
Monday 12/11-Tuesday 12/12: Right Triangle Trig Examples ; Right Triangle Trig Assignment
Summative Assessment Friday 12/8
Thursday 12/7: Inverse trig study sheet (ans key); quizzizz; Test Review Problems (an old test)-- check solutions
Wednesday 12/6: extended warm-up; quizzes returned
Monday 12/4: 5 appointments Review (check solutions) QUIZ TUESDAY
Friday 12/1: Precalc 2.3 Problem Set (quia)
Wednesday 11/29-Thursday 11/30: 4.6 Other Inverse Trig Functions (solutions) video QUIZ TUESDAY
Homework-- Section 4-6: Practice Exercises pp226-228 #1-3, 5-11 (odds), 12-18, 20-23, 28-29, 32, 39, 47. STARTS BOTTOM OF p2 of pdf!!!! (due Fri)
Hwk Hints:
1-3. Work backwards.
5. cos-1(1/9.7)=
7. see #5
9. Easy, but get into DEG mode.
11. see #5 and use DEG mode.
12. tan pi = 0, Arctan 0 = 0.
13-15. Easy—they just cancel out.
16-18. Like granny says, use a reference triangle.
20-22. Again, reference triangle.
23. Graph Tan-1x and then move it up 3 units.
28. Graph Csc-1x and then reflect all the negative y-values in the x-axis. In other words, any part of the graph below the x-axis gets reflected above the x-axis. Absolute value takes the negatives and makes them positives!
29. Any consecutive odd pi/2’s, like (pi/2, 3pi/2).
32. Plug in all the values and then use Tan-1 to solve for theta.
39. Reference Triangle
47. Reference Triangle
Monday 11/27-Tuesday 11/28 (The push to Christmas starts now!):
Inverse Trig Functions: Sine and Cosine (solutions to handout)
Homework: Section 4-5: Practice Exercises p220-221 #1-6, 11-13, 15-17, 20, 24, 29-31, 35, 43-44. (start with p6 of pdf, due Wed)
Hints:
1-4. Work backwards. Use the chart if you have to, but these should be memorized by now.
5-6. Calculator. Functions are ‘above’ sin and cos buttons.
11-12. Same as #5-6 but put in DEG mode.
13. Picture the y = Arccos x graph. What will 3x do to the x –values? What will +1 do to the y-values?
15. Be careful here. The back of the book is wrong in some of your texts! The answer is 0.33pi.
16-17. First quadrant—REAL EASY!
20. Look at the graph of y = Arccsin x (we did it in class). What happens when you add 1?
24. Think? How else could we “chop-up” the sine function to make it one-to-one?
29. Do the inside first.
30-31. Like Granny says, draw a reference triangle!
35. Set equal to zero, graph, and locate the zero.
43-44. Factor like a quadratic and use the zero product property.
Wednesday 11/22: 2.2 Problem Set
Tuesday 11/21: Marble Slides activity
Monday 11/20: Simple Harmonic Motion (solutions)
Homework: Section 4-7: Practice Exercises pp233-235 #1-9 (odds), 13-14, 17, 22, 25, 27, 30, 32, 33, 35. Problems start on p5 of pdf (due Wed)
Hints:
1-9 (odds). General sinusoid: y = a sin b(x-c) + d
amplitude = a, period = 2pi/b, frequency = 1/period.
The unit for the period is seconds/cycle, the unit for frequency is cycles/second or Hz.
13. a = 2.5, pd = 4pi/3 (hard to tell from graph)
14. pd = 3pi/2 (hard to tell from graph)
17. This should be a –cos function.
22. pd = 12.25 hrs.
25. pd = 2 sec
27. f = ¼ Hz
30. did in class.
32. f = 5 Hz, a = 40
33. d = 4 (sinusoidal axis), a = .35, pd = 5.4
35. a = 10, pd = 0.9, (0, -5) is a point on graph. Tricky, because it has a phase shift.
Quiz Friday
Thursday: 4.3 Review Problems (check solutions)
Wednesday: AT-PAC #1
Tuesday 11/4: Trig Scavenger Hunt
Hints: y = a sin b(x - c) + d
period = 2pi/b for sine, cosine, secant, and cosecant.
period = pi/b for tangent and cotangent.
Specific problems:
1. pd = 2pi/3;
2. pd = 4pi
3. Sine is shifted pi/4 right, cosine 3pi/4 right.
4. d = 1
5. d =-1/2
6. a = 3/2
7. a = 2 . Secant function
8. Tangent shifted pi/4 right
9. Cotangent shifted down 1
10. pd = pi/3.
11. pd = pi
12. d = -1, a = 2
Monday 11/13: Quia Problem Set: Collins's classes; Thompson's classes
Friday 11/10: Complete handout from Thursday. Check solutions. [Careful with #4, the asymptote should be at 3pi/4 (not pi/2). Typo on answer key.] If you're stuck watch a video: graphing cosecant; other trig functions.
Thursday 11/9: Graphing Csc and Sec (check solutions)
Wednesday 11/8: Secant and Cosecant Functions
Monday 11/6: Sine application
Friday 11/3: 1.6 Prob Set
Thursday 11/2: Getting Equations of Sine and Cosine; Quia (1.6 Prob Set)-- due end of day Fri.
Wednesday 11/1: Online activity: join.quizzizz.com
Tuesday 10/31: Graphing Sine and Cosine Notes (answer key) homework (check answers)
Monday 10/30: 4.1 Graphing Sine and Cosine
Wednesday 10/25-Thursday 10/26: 3.1-3.6 Review Problems (solns)
Trig Unit Review Problems (solns)
Tuesday 10/24: Quick Unit Circle Quiz. Continue 3.9 Verifying Trig Identities and Trig Unit Review Problems #2, 5, 15, 16.
Monday 10/23: 3.9 Verifying Trig Identities. Lots of Practice. 6 question Requiz Tuesday. Unit Circle Practice-- memorized angles and trig values-- pi/6, pi/4, pi/3, etc.. . Assign: Trig Review Problems #1, 3, 4, 7 and Unit Circle Practice.
Test #2: Friday 10/27-- Summative Assessment.
Friday 10/20: Short unit circle quiz; 1.5 Quia Problem Set
Wednesday 10/18-Thursday 10/19: 3.8 Trig Identities (solns); Trig Identities Worksheet (solns); Lots of Practice
Tuesday 10/17: 3.6 Functions of Special Angles 3; finish 3.7 Evaluating Trig Functions.
Monday 10/16: 3.6 Functions of Special and Quadrantal Angles (solns) 3.7 Evaluating Trig Functions
Assign: pp163-164 #1-19odds, 23-28, 39, 41, 49. (due Wed)
Help section 3-7:
Make sure your calculator is in the correct mode: DEGREE or RADIAN
1. too easy
3. sin(127+5/60+10/3600)
5. 1/cos18
7. see #5
9. see #3
11. too easy
13. no calculator on these!
15. work backwards, use cos-1(-0.5023). Find the answers in QII and QIII.
17. work backwards, use sin-1(0.8143). Find the answers in QI and QII.
19. work backwards, use tan-1(-0.2677). Find the answers in QII and QIV.
23. Gettin’ tougher here. sec theta = 1.1111 is equivalent to cos theta = 1/1.1111. Now work backwards, use cos-1(1/1.1111). Find the answers in QIII and QIV.
24-28. Similar to #23. Get the reciprocal to put in terms of sine, cosine, or tangent, and then work backwards. Pick the appropriate quadrants.
39. This factors like a trinomial: ( )( )=0. Then use the zero product property.
41. This is just a “real-world” application of this stuff. Just plug-in to the formula and solve for g.
49. The easiest way to do this is to put the function into y1 , graph it, and use the Calc-value feature of your calculator.
Thursday 10/12: Review Problems (check solutions), quiz Fri.
Wednesday 10/11: Trig Flashcards, quiz Friday
Tuesday 10/10: 3.6 Special Angles (solns)
Friday 10/6: 3.5 The Trigonometric Functions (solns) finish for HW
Thursday 10/5: finish 3.3 Practice Problems (solutions) ; Problem Set 1.4 (quia)
Wednesday 10/4: 3.4 Circular Functions (Solns)
Unit Circle-- Circle with a radius of 1 centered at the origin.
sinθ = y-coordinate on the unit circle
cos θ = x-coordinate on the unit circle
Homework: pp145-146 Practice Exercises #1-12, 18-36 (evens), 43. (1st 2 pages of pdf) (due Thursday)
Hwk Help Section 3-4:
1. These are quadrantal angles (they terminate on either the x- or y-axes). The answers should be -1, 0, or 1.
2. 225 deg is a 45 degree angle in the 3rd quadrant. Use your knowledge of 45-45-90 right triangles. (The sides are 1-1-sqrt2). 810 degrees = 720 + 90 so it is coterminal with 90 degrees.
4-9. Sine (y) is positive in QI and QII but negative in QIII and QIV. Cosine (x) is positive in QI and QIV, but negative in QII and QIII.
10-12. see Ex3, p143.
18. Draw a reference triangle and use the Pythagorean Theorem to find y. Then use the definitions of sine and cosine.
20. Cosine of anything is always less than or equal to 1 (it’s the x-coordinate on the unit circle).
22. Again, use the unit circle.
24. Express 0.8 as 4/5 and draw a reference triangle.
26-32ev. Use your unit circle and the fact that sine is positive in Quadrants I and II and negative in QIII and QIV. Why? Also, cosine is positive in QI and QIV and negative in QII and QIII.
34. On the unit circle, if x = 1, then what does y equal?
36. On the unit circle, if x = 0, then what are the 2 possible values for y?
43. There’s only 3 values for sine that you know right now—0, -1, and 1. These are the answers.
Tuesday 10/3: 3.3 Practice Problems (solutions) check solutions to Mon hwk.
Assign: Section 3-3: pp137-140 Practice Exercises #25, 27, 31, 33, 35, 41, 43, 45. (skip to p9 of the pdf) (due Wed)
Hints:
25. These are both angular velocities. Use dimensional analysis to get the units correct.
27. Convert degrees to radians and use V = r*theta/t. Make sure to get the units correct.
31. Convert diameter to radius (divide by 2). Convert revolutions to radians, then use V =rw.
check hwk solutions
Monday 10/2: 3.3 Linear and Angular Velocity (solutions)
Assignment: Section 3-3: pp137-140 Practice Exercises #1, 5, 6, 9, 10, 13, 15, 19, 21. (skip to p9 of the pdf) (due Tues)
1. 1 rev = 2pi radians
5-6. Use 1 rev = 2pi radians and 1 min = 60 sec
9-10. Use 1 rev = 2pi radians and 1 min = 60 sec
13-15. Use V =rw. Make sure to get the units correct.
19-21. Convert degrees to radians and use V = r*theta/t. Make sure to get the units correct.
Thursday 9/28: 3.2 Arc Length and Sector Area Practice Quia 1.3; Quiz Friday
Wednesday 9/27: 3.1-3.2 Angles and their Measures Practice A video.
pi Radians = 180 degrees.
Tuesday 9/26: 3.1 Angles and Their Measures . Assign: Finish back of sheet (solutions)
Monday 9/25: Worksheet: Special Right Triangles. Get 'em done. Work with others as necessary. Did you forget this stuff? Here's a video to help you.
Wednesday, 9/20: 5 Review Problems; catch up.
Tuesday 9/19: Quizlet activity; More Review Problems (in notebook, finish for HW). Check solutions.
Monday, 9/18: 1.2 Problem Set (quia) finish Unit One Review Packet (check solutions)
Friday 9/15: Unit One Review Packet
Thursday, 9/14: Greatest Integer Function and Inverse Functions. Tonight's assignment. check solutions.
Wednesday, 9/13: Function Scavenger Hunt
Monday, 9/11: Practice problems for Tuesday's Quiz
Friday, 9/8: . Desmos activity. Short quiz Tuesday.
Homework: Finish last 5 problems (last page) of Graphs and Transformations
Thursday, 9/7: Graphs and Transformations
some videos that might help: Graphing with transformations; How to find the domain of any function
Wednesday, 9/6: 1.4 Domain and Range (solutions) Some tips to help you determine the domain:
1. Vertical asymptotes occur at x-values that make the denominator equal zero (You cannot divide by zero!).
2. The number under the square root cannot be negative.
Check Solutions to Labor Day Weekend Assignment
Homework: Finish handout from class.
Tuesday, 9/5: Collect weekend assignment. 1st problem Set--quia
Thursday, 8/31: Exploration of Functions Day 2. More practice from yesterday. Wrap up of Exploration of Functions / Notes on Functions
*Homework: #2, 4, 6, 8. Give the graph and tell me about all the features: domain, range, increasing, decreasing, 1-1?, zeros, etc. Use Desmos Online Graphing Calculator as necessary.
Monday, 8/28: Welcome Back. Precalculus is the study of functions. We're going to start right in and look at some functions.
Function matching activity-- We'll look at everyday situations and try to match them up with functions (in the form of a graph and an equation).
Tuesday, 8/29: Wrap up function matching activity from yesterday, sign up for quia
Sign up for Quia
Step 1. Go to the Quia website at https://www.quia.com/web.
Step 2. Now, click the area labeled Students. When the next page appears, enter your username and password if you already have a Quia account. If you do not have an account, click the link Create my free account. Fill out the form that appears. Select "Student" as the account type. When you are done, press the Create my account button.
Step 3. You should now be in the Student Zone. Type in the class code (see below) in the text field and press the Add class button. Now you're done!
Class Codes:
- Thompson HPC 1 (Period 1 ): XHMFJ849
- Thompson HPC 2 (Period 4/5 ): CJDDTB767
- Thompson HPC 3 (Period 7/8 ): BRXNB794
- Collins (Period 2 ): AKKDFA689
- Collins (Period 9 ): ATF337
- Collins (Period 10 ): BAJPB346
Now that you have registered for your instructor's course, you can view your class web page, take quizzes, view your quiz results, view time spent on Quia activities, and read your instructor's feedback from your Quia account.
Follow these steps to view your results:
Step 1. Log in to your account. (Remember, go to the Quia Web home page at https://www.quia.com/web and click the area labeled Students.)
Step 2. Click on the class name
Wednesday, 8/30: Exploration of Functions Day 1. We want to see what you know about functions. Some vocab that you should be familiar with by the end of the week: function, relation, domain, range, increasing/decreasing, end behavior, continuity, symmetry, transformations, odd/even functions, zeros, intercepts, asymptotes, one-to-one.
Thursday, 8/31: Exploration of Functions Day 2. More practice from yesterday. Wrap up of Exploration of Functions / Notes on Functions
*Homework: #2, 4, 6, 8. Give the graph and tell me about all the features: domain, range, increasing, decreasing, 1-1?, zeros, etc. Use Desmos Online Graphing Calculator as necessary.