Question 1

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

Accepted Answer

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

Question 2

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

Accepted Answer

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

Question 3

Which statement about the graph of $$y = \sin$$^{-1}$$ x is $$true?

Accepted Answer

It is a reflection of $$y = \sin x$$ about the line $$y = x.$$

Question 4

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

Accepted Answer

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

Question 5

Which of the following is NOT in the range of $$y = \sin$$^{-1}$$ x$$?

Accepted Answer

$$\frac{3\pi}{4}$$

Question 6

If $$	heta = \sin$$^{-1}$$ \left( \frac{\sqrt{3}}{2} ight)$$, what is the value of $$	heta in $$radians?

Accepted Answer

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

Question 7

A function $$f(x)$$ passes the horizontal line test. Which of the following must be true?

Accepted Answer

It is one-to-one and has an inverse function.

Question 8

Given $$y = \sin$$^{-1}$$ x$$, which of the following is true for all $$x in $$the domain?

Accepted Answer

$$\sin(y) = x$$

Question 9

If $$y = \sin$$^{-1}$$ x$$, what is the range of $$y$$?

Accepted Answer

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

Question 10

Suppose $$y = \sin$$^{-1}$$ x$$ and $$x = \sin y. $$Which of the following is a correct statement about their graphs?

Accepted Answer

The graph of $$y = \sin$$^{-1}$$ x is a $$reflection of $$y = \sin x$$ about the line $$y = x.$$

Question 11

A real-world application: A ramp is built so that its height is 1 meter and its length along the ground is 2 meters. What is the angle $$	heta (in $$radians) that the ramp makes with the ground? (Use $$	heta = \sin$$^{-1}$$ \left( \frac{1}{2} ight).)$$

Accepted Answer

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

Question 12

Which of the following is the correct interpretation of $$y = \sin$$^{-1}$$ x$$?

Accepted Answer

The angle $$y$$ whose sine is $$x.$$

Question 13

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

Accepted Answer

$$0$$

Question 14

Which of the following statements is true about the inverse sine function?

Accepted Answer

Its domain is $$[-1, 1].$$

Question 15

If $$y = \sin$$^{-1}$$ x$$, which of the following is always true?

Accepted Answer

$$-1 \leq x \leq 1$$

Inverse Trigonometric Functions and Their Applications

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