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

Question 1

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

Accepted Answer

$$[-1, 1]$$

Question 2

What is the range of the inverse sine function $$y = \sin$$^{-1}$$x$$?

Accepted Answer

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

Question 3

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

Accepted Answer

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

Question 4

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

Accepted Answer

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

Question 5

For which values of $$x is$$ $$\sin$$^{-1}$$x$$ defined?

Accepted Answer

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

Question 6

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

Accepted Answer

$$\sin y = x$$

Question 7

Given $$y = \sin$$^{-1}$$x$$, what is the interval for $$y$$?

Accepted Answer

$$-\frac{\pi}{2} \leq y \leq \frac{\pi}{2}$$

Question 8

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

Accepted Answer

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

Question 9

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

Accepted Answer

$$-\frac{\pi}{2}$$

Question 10

Which of the following is NOT a property of inverse functions?

Accepted Answer

A function can have multiple inverses if it passes the horizontal line test.

Question 11

If $$\sin$$^{-1}$$(x) = \frac{\pi}{6}$$, what is the value of $$x$$?

Accepted Answer

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

Question 12

Which of the following statements is true about the domain and range of $$y = \sin$$^{-1}$$x$$?

Accepted Answer

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

Question 13

If $$y = \sin$$^{-1}$$x$$, which of the following is the correct composite function property?

Accepted Answer

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

Question 14

Which of the following is the correct value for $$\sin$$^{-1}$$(0)$$?

Accepted Answer

$$0$$

Question 15

If $$y = \sin$$^{-1}$$x$$, which of the following is a correct statement about $$y$$?

Accepted Answer

$$y is $$the angle in $$[-\frac{\pi}{2}, \frac{\pi}{2}]$$ whose sine is $$x.$$

Inverse Trigonometric Functions and Their Applications

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