AP®︎ Precalculus: Topic 3.9 Practice Test

Prepare for your quiz, test, or the AP exam with focused practice questions on Topic 3.9 of AP Precalculus – Inverse Trigonometric Functions.

Questions List

Topic 3.9

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Question 1 Easy

To define sin⁡−1x\sin^{-1} x, cos⁡−1x\cos^{-1} x and tan⁡−1x\tan^{-1} x, the domains of sine, cosine and tangent are restricted. Which choice gives the restricted domains of sine, cosine and tangent, in that order?

A[−π2,π2]\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]; [0,π][0, \pi]; [−π2,π2]\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]
B[0,π][0, \pi]; [−π2,π2]\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]; (−π2,π2)\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)
C[−π2,π2]\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]; [−π2,π2]\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]; (−π2,π2)\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)
D[−π2,π2]\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]; [0,π][0, \pi]; (−π2,π2)\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)

What You’re Being Tested On:

Explore the learning objectives taken directly from the College Board’s AP® Precalculus Curriculum. Ensure you’re prepared for the exact topics covered on the AP® exam, in-class tests, and quizzes, and gain confidence in your mastery of the material.

Topic 3.9: Inverse Trigonometric Functions

Learning Objective: 3.9.A

Construct analytical and graphical representations of the inverse of the sine, cosine, and tangent functions over a restricted domain.

Essential Knowledge: 3.9.A.1

For inverse trigonometric functions, the input and output values are switched from their corresponding trigonometric functions, so the output value of an inverse trigonometric function is often interpreted as an angle measure and the input is a value in the range of the corresponding trigonometric function.

Essential Knowledge: 3.9.A.2

The inverse trigonometric functions are called arcsine, arccosine, and arctangent (also represented as sin⁡−1x\sin^{-1}x, cos⁡−1x\cos^{-1}x, and tan⁡−1x\tan^{-1}x). Because the corresponding trigonometric functions are periodic, they are only invertible if they have restricted domains.

Essential Knowledge: 3.9.A.3

In order to define their respective inverse functions, the domain of the sine function is restricted to [−π2,π2]\left[-\frac{\pi}{2},\frac{\pi}{2}\right], the cosine function to [0,π][0,\pi], and the tangent function to (−π2,π2)\left(-\frac{\pi}{2},\frac{\pi}{2}\right).

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