Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 5 - Trigonometric Functions - Section 5.3 Properties of the Trigonometric Functions - 5.3 Assess Your Understanding - Page 418: 35


$\tan{\theta}=-\dfrac{3}{4}$ $\csc{\theta} =- \dfrac{5}{3}$ $\sec{\theta} =\dfrac{5}{4}$ $\cot{\theta} =-\dfrac{4}{3}$

Work Step by Step

$\tan{\theta}= \dfrac{\sin{\theta}}{\cos{\theta}}$ $\therefore \tan{\theta}= \dfrac{-\dfrac{3}{5}}{\dfrac{4}{5}}=-\dfrac{3}{4}$ $\csc{\theta} = \dfrac{1}{\sin{\theta}}$ $\therefore \csc{\theta} = \dfrac{1}{-\dfrac{3}{5}}=- \dfrac{5}{3}$ $\sec{\theta} = \dfrac{1}{\cos{\theta}}$ $\therefore \sec{\theta} = \dfrac{1}{\dfrac{4}{5}}= \dfrac{5}{4}$ $\cot{\theta} = \dfrac{1}{\tan{\theta}}$ $\therefore \cot{\theta} = \dfrac{1}{-\dfrac{3}{4}}= -\dfrac{4}{3}$
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