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

Given information

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

Rewriting using inverse rule and calculating

Calculating, we get

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

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

Using, we get

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

Short Answer

Step by step solution

Given information

Rewriting using inverse rule and calculating

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

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In Problems 79-90, find the exact value of each expression.csc2sin-1-35

Short Answer

Step by step solution

Given information

Rewriting using inverse rule and calculating

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Logic and Functions

Statistics

Geometry

Discrete Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

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