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: 4

Answer

0.30, 2.84, $2\pi$, $0.30+2k\pi$, $2.84+2k\pi$

Work Step by Step

We can find the solutions of $\sin x=0.3$ algebraically. First we find the solutions in the interval $[0, 2\pi)$. We get one such solution by taking $\sin^{-1}$ to get $x\approx 0.30$. The other solution in this interval is $x\approx 2.84$. We find all solutions by adding multiples of $2\pi$ to the solutions in $[0, 2\pi)$. The solutions are $0.30+2k\pi$ and $2.84+2k\pi$.
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