$\sin(\sin^{-1}x) = x$ \,\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

Study Guide - Practice Questions