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 6 - Analytic Trigonometry - Section 6.5 Sum and Difference Formulas - 6.5 Assess Your Understanding - Page 509: 79

Answer

$\frac{63}{65}$

Work Step by Step

1. Let $sin^{-1}(\frac{5}{13})=u$ (quadrant I), we have $sin(u)=\frac{5}{13}, cos(u)=\frac{12}{13}$ 2. Let $tan^{-1}(\frac{3}{4})=v$ (quadrant I), we have $tan(v)=\frac{3}{4}, sin(v)=\frac{3}{5}, cos(v)=\frac{4}{5}, $ 3. $cos(u-v)=cos(u)cos(v)+sin(u)sin(v)=(\frac{12}{13})(\frac{4}{5})+(\frac{5}{13})(\frac{3}{5})=\frac{63}{65}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.