Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 6 - Inverse Circular Functions and Trigonometric Equations - Section 6.1 Inverse Circular Functions - 6.1 Exercises - Page 266: 98


$cot~(arcsin~u) = \frac{\sqrt{1-u^2}}{u}$

Work Step by Step

Let $~~\theta = arcsin~u$ Then $~~sin~\theta = u$ $cot~\theta = \frac{cos~\theta}{sin~\theta}$ $cot~\theta = \frac{\sqrt{1-sin^2~\theta}}{sin~\theta}$ $cot~\theta = \frac{\sqrt{1-u^2}}{u}$ Therefore, $~~cot~(arcsin~u) = \frac{\sqrt{1-u^2}}{u}$
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