Answer
(a) $3$.
(b) $-9$.
Work Step by Step
Given $f(\theta)=cot\theta$ (an odd function) with $f(a)=cot(a)=-3$, we have:
(a) $f(-a)=-f(a)=3$.
(b) $f(a)+f(a+\pi)+f(a+4\pi)=cot(a)+cot(a+\pi)+cot(a+4\pi)=3cot(a)=-9$.
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)
by Sullivan III, Michael
Published by
Pearson
ISBN 10:
0-32193-104-1
ISBN 13:
978-0-32193-104-7
Chapter 5 - Trigonometric Functions - Section 5.3 Properties of the Trigonometric Functions - 5.3 Assess Your Understanding - Page 419: 116
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