Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 14 - Trigonometric Identities and Equations - 14-1 Trigonometric Identities - Practice and Problem-Solving Exercises - Page 909: 43


$$\cot\theta=\sqrt {\frac{1}{\sin^{2}\theta}-1}$$

Work Step by Step

Start with the Pythagorean Identity $$\csc^{2}\theta=1+\cot^{2}\theta.$$ Rearrange terms and solve for $\cot\theta$: $$\cot^{2}\theta=\csc^{2}\theta-1$$ $$\cot\theta=\sqrt {\csc^{2}\theta-1}.$$ Using the Reciprocal Identity $$\sin\theta=\frac{1}{\csc\theta},$$ substitute to obtain $$\cot\theta=\sqrt {\frac{1}{\sin^{2}\theta}-1}.$$
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