Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 6 - Section 6.2 - More on Trigonometric Equations - 6.2 Problem Set - Page 332: 14



Work Step by Step

$2sin(\theta)+sin(2\theta)=0$ $2sin(\theta)+2sin(\theta)cos(\theta)=0\;\;\;\;\;\;\;\;\;\;$ $2sin(\theta)\{1+cos(\theta)\}=0$ $2sin(\theta)=0\;\;\;\;\;\;\;\;\;\;\;\;or\;\;\;\;\;\;\;\;\;\;\;\;1+cos(\theta)=0$ $sin(\theta)=0$ $\theta= sin^{-1}(0)$ $\theta=0^o\;\;\;\;\;\;\;\;\;\;\;\;\;\;or\;\;\;\;\;\;\;\;\;\;\;\theta=180^o$ $1+cos(\theta)=0$ $cos(\theta)=-1\;\;\;\;\;\;\;\;\;\;$ subtract each side from $-1$. $sin(\theta)= \frac{1}{2}\;\;\;\;\;\;\;\;\;\;$ $\theta=cos^{-1}(-1)$ $\theta=0^o\;\;\;\;\;\;\;\;\;\;\;\;\;\;or\;\;\;\;\;\;\;\;\;\;\;\theta=180^o$ $\theta=\{0^o,180^o\}$
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