Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 4 - Section 4.4 - Trigonometric Functions of Any Angle - Exercise Set - Page 576: 99


The two values of $\theta $ are $\frac{\pi }{4}$ and $\frac{3\pi }{4}$.

Work Step by Step

We have the given expression: $\sin \theta =\frac{\sqrt{2}}{2}$. Here, the reference angle is $\frac{\pi }{4}$ and $\theta $ lies in quadrants I or II. Consider: the angle $\theta $ lies in quadrant I. $\theta =\frac{\pi }{4}$ Consider: the angle $\theta $ lies in quadrant II. $\begin{align} & \theta =\pi -\frac{\pi }{4} \\ & =\frac{4\pi -\pi }{4} \\ & =\frac{3\pi }{4} \end{align}$
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