Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 4 - Section 4.2 - Trigonometric Functions: The Unit Circle - Exercise Set - Page 548: 48


The value of the trigonometric function $\cot \left( -\frac{\pi }{4}+17\pi \right)$ is $-1$.

Work Step by Step

Consider the trigonometric function, $\cot \left( -\frac{\pi }{4}+17\pi \right)$ Use the property $\cot \left( t+n\pi \right)=\cot t$. Here, the value of $t$ is $-\frac{\pi }{4}$ and the value of $n$ is $17$. $\cot \left( -\frac{\pi }{4}+17\pi \right)=\cot \left( -\frac{\pi }{4} \right)$ Use the property $\cot \left( -t \right)=-\cot t$. $\cot \left( -\frac{\pi }{4}+17\pi \right)=-\cot \frac{\pi }{4}$ The value of $\cot \frac{\pi }{4}$ is $1$. So, $\cot \left( -\frac{\pi }{4}+17\pi \right)=-1$ Therefore, the value of the trigonometric function $\cot \left( -\frac{\pi }{4}+17\pi \right)$ is $-1$.
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