Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 6 - Inverse Circular Functions and Trigonometric Equations - Section 6.3 Trigonometric Equations II - 6.3 Exercises - Page 279: 16


The corresponding values of $\theta$ are $$\{135^\circ,180^\circ,225^\circ,270^\circ\}$$

Work Step by Step

1) The question asks for solutions over the interval $[0^\circ, 360^\circ)$, meaning that $$\theta\in[0^\circ,360^\circ)$$ or $$0^\circ\le\theta\lt360^\circ$$ 2) Now from also the question, your work leads to $$\frac{1}{3}\theta=45^\circ,60^\circ,75^\circ,90^\circ$$ To find corresponding values of $\theta$ from $\frac{1}{3}\theta$, we multiply both sides by $3$ $$\theta=135^\circ,180^\circ,225^\circ,270^\circ$$ 3) Finally, it is crucial to compare the values of $\theta$ in 2) with the range found in 1). We see that all four values of $\theta=135^\circ,180^\circ,225^\circ,270^\circ$ fit in the range of $\theta\in[0^\circ,360^\circ)$. None would be eliminated as a result. The corresponding values of $\theta$ are $$\{135^\circ,180^\circ,225^\circ,270^\circ\}$$
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