Objectives (click/tap to expand)
Solve right triangle problems
Solve simple harmonic motion problems
As also presented on Chapter 4.7 page:
Here is a pdf of fourTransformation Exercises that involve inverse trig functions, and are being used as your very reasonable Winter Break assignment.
Back to solving right triangle problems... of a slightly more difficult variety. The process in this video is similar to that in p427, Example 3, in our textbook.
Can you can find another way to do this problem, perhaps using cotangent instead of tangent, or looking at complementary angles? If I were to re-make this video, I would use cotangent instead of tangent since it makes the algebra a little neater... but then again, we shouldn't be afraid of a little messy algebra. Any valid method you choose to use is fine as long as you demonstrate good trigonometry and algebra practices.
Simple Harmonic Motion -- or, writing the sinusoidal functions that model real-world oscillations, vibrations, rotations, etc. Play around with the accompanying Geogebra constructions here.
Years ago when I made this video, I tended to do what most textbooks do: Jump from the word problem straight to the equation, and use a formula to relate the period to the "b" value in the equation.
If I were to re-make this video, I would reinforce my in-class messaging by insisting that students:
Draw a graph first after interpreting the word problem, and use that graph to then develop the equation
Rely on your knowledge of transformations rather then memorize some "dumb formula" for period
In case you don't have it from class, here is the Simple Harmonic Motion handout. You may look to the textbook for extra exercises, but there are some aspects about the book's exercises that I find distract from the skills I want you to practice.
Also, here are a couple more practice questions to prepare you for the upcoming test, as handed out in class. One involves finding the maximum "viewing angle," or "kicking angle" in this exercise. The other is one final "Batman Equation" exercise. The solutions are on the second page.
As provided in the Lessons document, here are the exercises you were assigned for homework in these sections of the book. Links to the various handouts are provided on the Chapter 4.7 and 4.8 webpages. The assessment will draw from this content.
p423: 1, 2, 5, 6, 9, 10, 13, 14, 17, 18, 23-32 (Evaluating inverse trig expressions, with and without calculator)
p424: 34-52 except multiples of 3 ("Analyze each function" as we did in Q1, describe transformations, find algebraic expression equivalent to a composite trig expression)
p432: 1-5, 14-16, 23, 24, 25 (Solve right-triangle trig problems of varying difficulty levels)
Go to next page, Chapter 5.1.