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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 7: Q. 90 (page 496)

In Problems 79-90, find the exact value of each expression.
$\csc [2 \sin^{- 1} (- \frac{3}{5})]$

Short Answer

Expert verified

The exact value is $- \frac{25}{24}$

Step by step solution

01

Given information

Given expression $\csc [2 \sin^{- 1} (- \frac{3}{5})]$

02

Rewriting using inverse rule and calculating

Calculating, we get

$\sin (\sin^{- 1} x) = x \sin^{- 1} x = \cos^{- 1} (\sqrt{1 - x^{2}}) a = \csc (2 \sin^{- 1} (- \frac{3}{5})) 胃 = \sin^{- 1} (- \frac{3}{5}) 胃 = \cos^{- 1} (\frac{4}{5})$

03

Using double angle formula, we geta=csc2sin-1-35a=12sinsin-1-35coscos-145a=12-3545a=-2524

Using, we get

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Most popular questions from this chapter

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