AP®︎ Precalculus: Topic 3.11 Practice Test

Prepare for your quiz, test, or the AP exam with focused practice questions on Topic 3.11 of AP Precalculus – The Secant, Cosecant, and Cotangent Functions.

Questions List

Topic 3.11

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Question 1 Easy

For an angle θ\theta, sin⁡θ=35\sin\theta = \frac{3}{5} and cos⁡θ=−45\cos\theta = -\frac{4}{5}. What is the value of sec⁡θ\sec\theta?

A−54-\frac{5}{4}
B−43-\frac{4}{3}
C53\frac{5}{3}
D−34-\frac{3}{4}

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 3.11: The Secant, Cosecant, and Cotangent Functions

Learning Objective: 3.11.A

Identify key characteristics of functions that involve quotients of the sine and cosine functions.

Essential Knowledge: 3.11.A.1

The secant function, f(θ)=sec⁡θf(\theta) = \sec \theta, is the reciprocal of the cosine function, where cos⁡θ≠0\cos \theta \ne 0.

Essential Knowledge: 3.11.A.2

The cosecant function, f(θ)=csc⁡θf(\theta) = \csc \theta, is the reciprocal of the sine function, where sin⁡θ≠0\sin \theta \ne 0.

Essential Knowledge: 3.11.A.3

The graphs of the secant and cosecant functions have vertical asymptotes where cosine and sine are zero, respectively, and have a range of (−∞,−1]∪[1,∞)(-\infty, -1] \cup [1, \infty).

Essential Knowledge: 3.11.A.4

The cotangent function, f(θ)=cot⁡θf(\theta) = \cot \theta, is the reciprocal of the tangent function, where tan⁡θ≠0\tan \theta \ne 0. Equivalently, cot⁡θ=cos⁡θsin⁡θ\cot \theta = \frac{\cos \theta}{\sin \theta}, where sin⁡θ≠0\sin \theta \ne 0.

Essential Knowledge: 3.11.A.5

The graph of the cotangent function has vertical asymptotes for domain values where tan⁡θ=0\tan \theta = 0 and is decreasing between consecutive asymptotes.

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