## Trigonometry 7th Edition

Published by Cengage Learning

# Chapter 1 - Section 1.4 - Introduction to Identities - 1.4 Problem Set - Page 41: 53

#### Answer

$\sin{\theta} =\dfrac{1}{a}$ $\cos{\theta} =\dfrac{\sqrt{a^2-1}}{a}$ $\tan{\theta} = \dfrac{1}{\sqrt{a^2-1}}$ $\csc{\theta} = a$ $\sec{\theta} =\dfrac{a}{\sqrt{a^2-1}}$ $\cot{\theta} =\sqrt{a^2-1}$

#### Work Step by Step

$\csc{\theta} = a$ $\sin{\theta} = \dfrac{1}{\csc{\theta}} = \dfrac{1}{a}$ $\because \theta \in QI \hspace{20pt} \therefore \cos{\theta}$ is positive. $\cos{\theta} = \sqrt{1-\sin^2{\theta}} = - \sqrt{1-\left(\dfrac{1}{a}\right)^2} = \sqrt{\dfrac{a^2-1}{a^2}} = \dfrac{\sqrt{a^2-1}}{a}$ $\tan{\theta} = \dfrac{\sin{\theta}}{\cos{\theta}} = \dfrac{1}{\sqrt{a^2-1}}$ $\sec{\theta} = \dfrac{1}{\cos{\theta}} = \dfrac{a}{\sqrt{a^2-1}}$ $\cot{\theta} = \dfrac{1}{\tan{\theta}}= \sqrt{a^2-1}$

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