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 550: 102


The value of given expression is $1$.

Work Step by Step

The sine function has periodicity of $2\pi $. So, $\begin{align} & f\left( a+2\pi \right)=f\left( a \right) \\ & f\left( a+4\pi \right)=f\left( a \right) \\ & f\left( a+6\pi \right)=f\left( a \right) \\ \end{align}$ Put all the values of the above in the main expression: $\begin{align} & f\left( a \right)+f\left( a+2\pi \right)+f\left( a+4\pi \right)+f\left( a+6\pi \right)=f\left( a \right)+f\left( a \right)+f\left( a \right)+f\left( a \right) \\ & =4f\left( a \right) \\ & =4\times \frac{1}{4} \\ & =1 \end{align}$ Thus, the value of the given expression is $1$.
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