Trigonometry (11th Edition) Clone

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

Chapter 1 - Trigonometric Functions - Section 1.4 Using the Definitions of the Trigonometric Functions - 1.4 Exercises - Page 38: 84

Answer

The cosecant and cotangent functions are undefined. The other function values are: $\cos\theta=1$ $\sin\theta=0$ $\sec\theta=1$ $\tan\theta=0$

Work Step by Step

$\cos\theta=1$ $\sin^{2}\theta+\cos^{2}\theta=\sin^{2}\theta+1^{2}=1$ $\implies \sin^{2}\theta=0$ or $\sin\theta=0$ $\sec\theta=\frac{1}{\cos\theta}=\frac{1}{1}=1$ $\csc\theta=\frac{1}{\sin\theta}=\frac{1}{0}$ As denominator vanishes, $\csc\theta$ is undefined. $\cot\theta=\frac{\cos\theta}{\sin\theta}=\frac{1}{0}$ is also undefined. $\tan\theta=\frac{\sin\theta}{\cos\theta}=\frac{0}{1}=0$
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