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: 83

Answer

The tangent and secant functions are undefined. The other function values are: $\sin\theta=1$ $\csc\theta=1$ $\cos\theta=0$ $\cot\theta=0$

Work Step by Step

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