## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 5 - Section 5.5 - Trigonometric Equations - Exercise Set - Page 704: 80

#### Answer

$x=\frac{\pi}{2}$

#### Work Step by Step

Step 1. Using the Sum-to-Product Formula $sin(u)+sin(v)=2sin(\frac{u+v}{2})cos(\frac{u-v}{2})$, the equation becomes $2sin(x)cos(\frac{\pi}{3})=1$ or $sin(x)=1$. Step 2. For $sin(x)=1$, we can find all x-values in $[0,2\pi)$ as $x=\frac{\pi}{2}$

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