Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 6 - Analytic Trigonometry - Chapter Review - Review Exercises - Page 528: 80

Answer

$2.90$

Work Step by Step

We know that $\cot {a}=\dfrac{1}{\tan {(a)}}$. This can also be written as: $\cot^{-1} {a}=\tan^{-1} (\dfrac{1}{a})$ In order to get the answer in radians, we want to set the calculator in radians mode, and use the inverse cosine function (round off the result to two decimal places) to obtain: $\cot^{-1} (4) =\tan^{-1} (\dfrac{-1}{4})=-0.2450 \approx -0.25$ The equation $\tan \theta=-0.25$ implies that that $\theta$ lies in quadrant II, but the answer we got is in quadrant IV. So we need to add $\pi$ to the answer to convert it to quadrant II. That is, $-0.25+\pi=2.90$
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