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

Study Guide - Practice Questions

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