Q: Which of the following is the reciprocal identity for $$\tan \theta$$?

$$\tan \theta = \frac{1}{\cot \theta}$$

Q: Which of the following is the correct reciprocal identity for $$\sec \theta$$?

$$\sec \theta = \frac{1}{\cos \theta}$$

Question 1

Which of the following best describes an angle in standard position?

Accepted Answer

Its initial side is on the positive x-axis and its terminal side is anywhere in the plane.

Question 2

Convert $$120^\circ to $$radians.

Accepted Answer

$$\frac{2\pi}{3}$$

Question 3

Given a right triangle with legs of length 3 and 4, what is the value of $$\sin 	heta$$ where $$	heta is $$the angle opposite the side of length 3?

Accepted Answer

$$\frac{3}{5}$$

Question 4

Which of the following is the reciprocal identity for $$	an 	heta$$?

Accepted Answer

$$	an 	heta = \frac{1}{\cot 	heta}$$

Question 5

A ladder leans against a wall forming a $$60^\circ$$ angle with the ground. If the ladder is 10 ft long, how high up the wall does it reach? (Round to two decimal places.)

Accepted Answer

$$10 \sin 60^\circ = 8.66 ft$$

Question 6

What is the period of the function $$y = \sin \left( \frac{1}{2}x \right)$$?

Accepted Answer

$$4\pi$$

Question 7

Which of the following is the correct cofunction identity for $$\sin A$$?

Accepted Answer

$$\sin A = \cos (90^\circ - A)$$

Question 8

A triangle has angles $$x$$ and $$y$$ such that $$x + y = 90^\circ. If$$ $$\sin x = 0.6$$, what is $$\cos y$$?

Accepted Answer

$$0.6$$

Question 9

If $$	an 	heta = \frac{5}{12} in a $$right triangle, what is $$\sin 	heta$$?

Accepted Answer

$$\frac{5}{13}$$

Question 10

Which transformation will shift the graph of $$y = \sin x up by 3 $$units?

Accepted Answer

$$y = \sin x + 3$$

Question 11

What is the amplitude of the function $$y = -2 \cos x$$?

Accepted Answer

$$2$$

Question 12

A 45-45-90 triangle has legs of length 7. What is the length of the hypotenuse?

Accepted Answer

$$7\sqrt{2}$$

Question 13

Which of the following is the correct value for $$\sin 45^\circ$$?

Accepted Answer

$$\frac{\sqrt{2}}{2}$$

Question 14

If $$\cos 	heta = 0.5$$ and $$0^\circ \u003c 	heta \u003c 90^\circ$$, what is $$	heta$$?

Accepted Answer

$$60^\circ$$

Question 15

Which of the following is the period of $$y = 	an x$$?

Accepted Answer

$$\pi$$

Question 16

A 30-60-90 triangle has a short leg of length 5. What is the length of the hypotenuse?

Accepted Answer

$$10$$

Question 17

If $$\sin 	heta = 0.8$$, what is $$	heta in $$degrees? (Round to the nearest degree.)

Accepted Answer

$$53^\circ$$

Question 18

Which of the following is the correct reciprocal identity for $$\sec 	heta$$?

Accepted Answer

$$\sec 	heta = \frac{1}{\cos 	heta}$$

Question 19

A Ferris wheel has a radius of 20 meters. What is the height above the center of a seat at an angle of $$150^\circ$$ from the horizontal?

Accepted Answer

$$20 \sin 150^\circ = 10$$ meters

Trigonometry Study Guide: Angles, Trigonometric Functions, and Graphs

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