Math 4 Unit 6: Trigonometry

Sine

Solve for y

sin(5) = 2/y

y = 2/sin(5) = 22.95 ft

Cosine

Solve for y.

cos(38) = y/12

y = 12cos(38) = 9.5cm

Tangent

Solve for x.

tan(5) = 2/x

x = 2/tan(5) = 22.86 ft

Angle of Elevation or Depression

tan(50) = x/45

x = 45tan(50) = 53.63 feet

Law of Sines

Find the length of AB.

sin(70)/15 = sin(45)/AB

AB = 15sin(45)/sin(70) = 11.29

Law of Cosines

Find the length of the missing side.

x^2 = 400^2 + 375^2 - 2*400*375*cos35

= 54879.39

x = 234.26 m

Law of Cosines Application

Two ships are sailing from Halifax. The Nina is sailing due east and the Pinta is sailing 43° south of east. After an hour, the Nina has traveled 115km and the Pinta has traveled 98km. How far apart are the two ships?

x^2 = 115^2 + 98^2 - 2*115*98*cos43

= 6344.29

x = 79.65 km

6 Trig Ratios

Find the 6 trig ratios of triangle formed by (-8, 6) in simplest radical form.

sinx = 3/5
cosx = -4/5
tanx = -3/4
cscx = 5/3
secx = -5/4
cotx = -4/3

Drawing Angles + Finding Coterminals

Draw 630 degrees, find the reference angle, and find a positive coterminal angle from 0 - 360 degrees.

550 - 360 = 190

Draw -70 degrees, find the reference angle, and find a positive coterminal angle from 0 - 360 degrees.

-70 + 360 = 290

Converting Radians to Degrees

Convert 5pi/6 radians to degrees

Converting Degrees to Radians

Convert 225 degrees to radians

Evaluating Trigonometric Functions and Inverses using the Unit Circle

Evaluate sin135. Answer: sqrt2/2

Evaluate cos45. Answer: sqrt2/2

Evaluate tan210. Answer: sqrt3/3

Evaluate csc60. Answer: 2sqrt3/3

Evaluate sec180. Answer: -1

Evaluate cot315. Answer: -1

Evaluate sin-1 of 1/2. Answer: pi/6

Evaluate cos-1 of sqrt2/2. Answer: pi/4

Evaluate tan-1 of 0. Answer: 0, 2pi

Solving Trigonometric Equations

Solve for x on the interval [0, 2pi]

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