Answer
$\frac{2\sqrt 6}{7}$
Work Step by Step
Let $csc^{-1}\frac{7}{5}=t$, we have $csc(t)=\frac{7}{5}, sin(t)=\frac{5}{7}$ and $cos(t)=\sqrt {1-sin^2t}=\frac{2\sqrt 6}{7}$
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)
by Sullivan III, Michael
Published by
Pearson
ISBN 10:
0-32193-104-1
ISBN 13:
978-0-32193-104-7
Chapter 6 - Analytic Trigonometry - Section 6.7 Product-to-Sum and Sum-to-Product Formulas - 6.7 Assess Your Understanding - Page 525: 59
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