Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 6 - Section 6.4 - Inverse Trigonometric Functions and Right Triangles - 6.4 Exercises - Page 506: 5

Answer

a) $\pi /2$ b) $\pi/2$ c) $\pi /3$

Work Step by Step

First, one must find the intervals of each function. For sin$^{-1}$ is $-\frac{\pi}{2} \leq x \leq \frac{\pi}{2}$. For tan$^{-1}$ is also $-\frac{\pi}{2} \leq x \leq \frac{\pi}{2}$. And for cos$^{-1}$ is $0 \leq x \leq \pi$ Then, one must find the angle that gives the y-value in sin$^{-1}$, x-value in cos$^{-1}$, or the slope in tan$^{-1}$, and that fits inside the given intervals.
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