Question 1

Which of the following is the correct domain for the function $$f(x) = 	an x$$?

Accepted Answer

All real numbers except odd multiples of $$\frac{\pi}{2}$$

Question 2

Given the function $$y = 3\sin(2x - \frac{\pi}{2})$$, what is the amplitude, period, and phase shift?

Accepted Answer

Amplitude: $$3$$, Period: $$\pi$$, Phase shift: $$\frac{\pi}{4}$$ left

Question 3

Which of the following statements about the graph of $$y = \cos x is $$TRUE?

Accepted Answer

It is an even function with period $$2\pi.$$

Question 4

Evaluate $$\sin$$^{-1}$$\left(\frac{\sqrt{3}}{2}\right).$$

Accepted Answer

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

Question 5

If $$	an$$^{-1}$$(1) = 	heta$$, what is the value of $$	heta in $$the principal range?

Accepted Answer

$$\frac{\pi}{4}$$

Question 6

Which of the following is the correct range for $$f(x) = \sec x$$?

Accepted Answer

$$(-\infty, -1] \cup [1, \infty)$$

Question 7

A ladder leans against a wall making an angle of $$60^\circ$$ with the ground. If the ladder is $$10 ft $$long, how high up the wall does it reach?

Accepted Answer

$$10 \sin 60^\circ = 5\sqrt{3} ft$$

Question 8

Which of the following is undefined?

Accepted Answer

$$	an(\frac{\pi}{2})$$

Question 9

If $$\sin 	heta = \frac{3}{5}$$ and $$	heta is in $$the first quadrant, what is $$\cos 	heta$$?

Accepted Answer

$$\frac{4}{5}$$

Question 10

Which transformation will shift the graph of $$y = \sin x to $$the right by $$\frac{\pi}{3}$$ units?

Accepted Answer

$$y = \sin(x - \frac{\pi}{3})$$

Question 11

What is the period of the function $$y = 	an x$$?

Accepted Answer

$$\pi$$

Question 12

If $$\cos$$^{-1}$$(x) = \frac{\pi}{3}$$, what is the value of $$x$$?

Accepted Answer

$$\frac{1}{2}$$

Question 13

Which of the following is the correct composition: $$\sin(\cos$$^{-1}$$(\frac{1}{2}))$$?

Accepted Answer

$$\frac{\sqrt{3}}{2}$$

Question 14

A ramp rises $$4$$ feet over a horizontal distance of $$12$$ feet. What is the angle of elevation of the ramp (to the nearest degree)?

Accepted Answer

$$	an$$^{-1}$$(\frac{1}{3})$$

Question 15

Which of the following is the correct range for $$f(x) = \sin$$^{-1}$$ x$$?

Accepted Answer

$$[-\frac{\pi}{2}, \frac{\pi}{2}]$$

Question 16

If $$\sin$$^{-1}$$(x) is $$defined, which of the following must be true?

Accepted Answer

$$x \in [-1, 1]$$

Question 17

If $$	an 	heta = 2$$ and $$	heta is in $$the second quadrant, what is $$\sin 	heta$$?

Accepted Answer

$$\frac{2}{\sqrt{5}} ($$but negative in Q2)

Question 18

Which of the following is true about the function $$y = \cot x$$?

Accepted Answer

It is undefined at multiples of $$\pi.$$

Question 19

If $$\sin(	heta) = -\frac{1}{2}$$ and $$	heta is in $$the fourth quadrant, what is $$	heta$$?

Accepted Answer

$$-\frac{\pi}{6}$$

Precalculus Study Guide: Trigonometric Functions and Their Applications (Sections 5.4–5.8)

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