Question 1

Convert $$96^{\circ} to $$radians.

Accepted Answer

$$\dfrac{8\pi}{15}$$

Question 2

Which of the following is the degree measure of $$\dfrac{5\pi}{12}$$ radians?

Accepted Answer

$$75^{\circ}$$

Question 3

Evaluate $$\sin\left(\dfrac{2\pi}{3}\right).$$

Accepted Answer

$$\dfrac{\sqrt{3}}{2}$$

Question 4

A particle starts at $$(1,0) on $$the unit circle and is rotated through an angle of $$\dfrac{27\pi}{4}$$ radians. In which quadrant does it end up?

Accepted Answer

Quadrant II

Question 5

If $$	an 	heta = -\dfrac{1}{2}$$ and $$\cos 	heta \u003e 0$$, what is $$\sin 	heta$$?

Accepted Answer

$$-\dfrac{1}{\sqrt{5}}$$

Question 6

Given $$\sin 	heta = -\dfrac{1}{3}$$ and $$\dfrac{\pi}{2} \u003c 	heta \u003c \dfrac{3\pi}{2}$$, find $$\cot 	heta.$$

Accepted Answer

$$2\sqrt{2}$$

Question 7

If $$\cos 	heta \u003e 0$$ and $$\cot 	heta \u003c 0$$, in which quadrant does $$	heta$$ lie?

Accepted Answer

Quadrant IV

Question 8

The point $$(2, -3)$$ lies on the terminal side of angle $$	heta. $$What is $$\csc 	heta$$?

Accepted Answer

$$-\dfrac{\sqrt{13}}{3}$$

Question 9

Which of the following is an equivalent form of the Pythagorean identity $$\sin^2$ x + \cos^2$ x = 1$$?

Accepted Answer

$$1 + 	an^2$ x = \sec^2$ x$$

Question 10

For $$f(x) = -2\sin(3x)$$, what is the period of the function?

Accepted Answer

$$\dfrac{2\pi}{3}$$

Question 11

Find the inverse function $$f^{-1}(x$$)$$ for f(x) = 2$$\sin x - 1$$, x$$ \in \left[ -\dfrac{\pi}{2}, \dfrac{\pi}{2} \right]$$.

Accepted Answer

$$f^{-1}(x$$) = \$$sin^{-1}$$\left(\dfrac{x+1}{2}\right)$$

Question 12

Solve for $$x$$: $$3\sin$$^{-1}$$(7x) = -\pi.$$

Accepted Answer

$$-\dfrac{\sqrt{3}}{14}$$

Question 13

Which of the following is the range of $$f(x) = 2\sin x - 1$$, $$x \in \left[ -\dfrac{\pi}{2}, \dfrac{\pi}{2} \right]$$?

Accepted Answer

$$[-3, 1]$$

Question 14

If $$	an 	heta = 1/2$$ and $$\sin 	heta \u003c 0$$, which quadrant does $$	heta$$ lie in?

Accepted Answer

Quadrant III

Question 15

Evaluate $$\cos$$^{-1}$$\left(\dfrac{1}{2}\right).$$

Accepted Answer

$$\dfrac{\pi}{3}$$

Question 16

For $$f(x) = \cos\left(\dfrac{x}{2}\right)$$, what is the period?

Accepted Answer

$$4\pi$$

Question 17

Solve for $$x$$: $$6\cos$$^{-1}$$(2x) = -\pi.$$

Accepted Answer

$$\dfrac{1}{4}$$

Question 18

Which of the following is the amplitude of $$f(x) = -2\cos(3x)$$?

Accepted Answer

$$2$$

Question 19

Which of the following is NOT a Pythagorean identity?

Accepted Answer

$$	an^2$ x - \sec^2$ x = 1$$

Precalculus Trigonometry and Inverse Functions Study Guide

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