Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 6 - The Circular Functions and Their Graphs - 6.2 The Unit Circle and Circular Functions - 6.2 Exercises: 73

Answer

$s=\dfrac{7\pi}{4}$

Work Step by Step

Use the inverse tangent function of a calculator in radian mode to obtain: $s =\tan^{-1}{(-1)}=-\frac{1}{4}\pi$ Since the angle must be within the interval $[\frac{3\pi}{2}, 2\pi]$, find the positive coterminal angle of $-\frac{1}{4}\pi$ in Quadrant IV. This angle can be found by adding $2\pi$ to the given angle to obtain: $-\frac{1}{4}\pi + 2\pi = -\frac{1}{4}\pi+\frac{98}{4}\pi=\frac{7}{4}\pi$ Thus, $-\frac{1}{4}\pi$ and $\frac{7}{4}\pi$ are coterminal angles and therefore have the same tangent value. Thus, $s=\dfrac{7\pi}{4}$
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