Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 1 - Section 1.4 - Introduction to Identities - 1.4 Problem Set - Page 41: 57

Answer

$\sin{\theta} =0.59$ $\cos{\theta} = -0.81$ $\tan{\theta} =-0.73$ $\csc{\theta} =1.69$ $\sec{\theta} = -1.24$ $\cot{\theta} =-1.37 $

Work Step by Step

$\sec{\theta} = -1.24$ $\cos{\theta} = \dfrac{1}{\sec{\theta}} = -\dfrac{1}{1.24} \approx -0.81$ $\because \theta \in QII \hspace{20pt} \therefore \sin{\theta}$ is positive. $\sin{\theta} = \sqrt{1-\cos^2{\theta}} = - \sqrt{1-(-0.81)^2} \approx 0.59$ $\tan{\theta} = \dfrac{\sin{\theta}}{\cos{\theta}} = \dfrac{0.59}{-0.81} \approx -0.73$ $\csc{\theta} = \dfrac{1}{\sin{\theta}} = \dfrac{1}{0.59} \approx 1.69$ $\cot{\theta} = \dfrac{\cos{\theta}}{\sin{\theta}} = \dfrac{-0.81}{-0.59} \approx -1.37 $
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