Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 5 - Section 5.5 - Inverse Trigonometric Functions and Their Graphs - 5.5 Exercises - Page 445: 41



Work Step by Step

The value is not in the quadrant we want it to be in. When we refer back to the unit circle we see that $2\pi/3$ is in quadrant 2. Arctan isn't defined there unfortunately. So we look for a value for which tan's value stays the same but in the 4th or 1st quadrant. To do this, on your unit circle draw a line through $2\pi/3$ and the center and extend it so that it hits another point on the circle. When we do so we get $-\pi/3$.
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