Question 1

Which of the following is the correct domain and range for the function $$y = \sin$$^{-1}$$ x$$?

Accepted Answer

Domain: $$[-1, 1]$$, Range: \left[ -\frac{\pi}{2}, \frac{\pi}{2} \right]$

Question 2

Evaluate $$\sin$$^{-1}$$ \left( \frac{\sqrt{3}}{2} \right)$$ and select the correct answer.

Accepted Answer

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

Question 3

Which of the following statements is true about the function $$f(x) = \cos x$$?

Accepted Answer

$$\cos(-x) = \cos(x)$$, so cosine is an even function.

Question 4

Given $$y = -2 \sin \left( \frac{\pi}{2} - 3x \right)$$, which of the following is an equivalent expression?

Accepted Answer

$$2 \sin 3 \left( x - \frac{\pi}{6} \right)$$

Question 5

If $$f(x) = x^2$, what is f(-2$$)$$?

Accepted Answer

$$4$$

Question 6

Which of the following is the correct definition of the inverse cosine function?

Accepted Answer

$$y = \cos$$^{-1}$$ x$$ iff $$\cos y = x$$ where $$x \in [-1, 1]$$ and $$y \in [0, \pi]$$

Question 7

Which of the following is the correct range for $$y = \sin x$$?

Accepted Answer

$$[-1, 1]$$

Question 8

If $$f(x) is $$one-to-one, which of the following must be true for its inverse $$f^{-1}(x$$)$$ to exist?

Accepted Answer

$$f$$ passes both the horizontal and vertical line tests.

Question 9

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

Accepted Answer

$$\frac{5\pi}{6}$$

Question 10

Which of the following is true about the periodicity of trigonometric functions and their inverses?

Accepted Answer

Trigonometric functions are periodic and not one-to-one, so their inverses are defined only on restricted domains.

Question 11

Given $$y = \sin$$^{-1}$$ \left( -\frac{\sqrt{2}}{2} \right)$$, what is the exact value of $$y$$?

Accepted Answer

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

Question 12

Which of the following is the correct general form for a sine function with amplitude $$a$$, frequency $$b$$, and phase shift $$c$$?

Accepted Answer

$$y = a \sin b(x - c)$$

Question 13

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

Accepted Answer

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

Question 14

Which of the following points represents the coordinates on the unit circle for $$	heta = \frac{\pi}{3}$$?

Accepted Answer

$$\left( \frac{1}{2}, \frac{\sqrt{3}}{2} \right)$$

Question 15

If $$y = \sin$$^{-1}$$(0)$$, what is the value of $$y$$?

Accepted Answer

$$0$$

Question 16

Which of the following is the correct relationship for the inverse sine function?

Accepted Answer

$$\sin(\sin$$^{-1}$$ x) = x$$ for $$x \in [-1, 1]$$

Question 17

Given $$y = \cos$$^{-1}$$(1)$$, what is the value of $$y$$?

Accepted Answer

$$0$$

Question 18

If $$f(x) = x^2$ and g(x$$) = \sqrt{x}$$, which of the following statements is true about their inverses?

Accepted Answer

$$g(x) is $$one-to-one and has an inverse on $$[0, \infty).$$

Question 19

Which of the following is the correct value for $$	an$$^{-1}$$(-1)$$?

Accepted Answer

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

Study Guide: Trigonometric Functions and Their Inverses in Precalculus

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