Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 7 - Section 7.4 - Basic Trigonometric Equations - 7.4 Exercises - Page 569: 36

Answer

$0.34+k\pi$, $2.80+k\pi$

Work Step by Step

$9\sin^2\theta-1=0$ $9\sin^2\theta=1$ $\sin^2\theta=\frac{1}{9}$ $\sin\theta=\pm\frac{1}{3}$ If $\sin\theta=\frac{1}{3}$, then $\theta=0.34+2k\pi$ or $\theta=2.80+2k\pi$. If $\sin\theta=-\frac{1}{3}$, then $\theta=3.48+2k\pi$ or $\theta=5.94+2k\pi$. Combining the two, we get $\theta=0.34+k\pi$ or $\theta=2.80+k\pi$.
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