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Basic Trig Review

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Student ID____________

Trig ReviewProfessor O. LePoint

Instructions: Answer the following questions. You can use calculators. Complete as many questions as you can.

Question 1: Give the definition for the following in the space provided below:

• Vertical Asymptotes of y = tan x

• Supplementary Angles

• Reference Angle

• SOH CAH TOA

• Inverse Function

Question 2: Find the convert 18° to π radians and find 2 coterminal angles in

radians. Show all work.

Question 3: The following two triangles are similar. Find x and y.Hint: Draw the triangles separately. Your answers will be in variables.

Question 4: What is the sine, cosine, and tangent values of θ in standard position

if the terminal side of θ is defined by x+2y =0, for x≥ 0. Box your answers.

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10

20

74°

X - 5

X +y

X -2y

74°

Question 5:

Give the fractions for the following trigonometric functions using the figure. Give the restrictions.

If θ = tan -1 u

• Sin θ = __________________________________

• cos θ = __________________________________

• cot θ = __________________________________

Question 6 : Give the exact value of the expression without using a calculatorcos ( tan -1 5/12 - tan -1 3/4 ).

Question 7:Write sin 2θ – sin 4θ as a product of two functions.

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θ

Question 8:

Use the half angle identity to find cos (-22.5°).

Question 9 : Graphing y = 2 sin (2x) + 1• What is the period of y = 2 sin (2x) + 1 ?

• Evaluate y = 2 sin (2x) + 1 , on an interval starting with 0 and ending with π.

• Sketch y = 2 sin (2x) + 1 in the space provided below

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4

3

2

4

4

3

1

2

3

0

CONTINUED

Question 10:

The Hubble telescope traveling in a circular orbit 1600 km above the surface of the Earth takes 2 hours to make an orbit. The radius of earth is 6400 km.

• Find the linear speed of the telescope. Show all work and equations.

• Find the distance the telescope travels in 4.5 hours. Show all work and equations.

Question 11:

Graph y= sin x

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6400

1600