Chapter 7: Q. 85 (page 496)

In Problems 79-90, find the exact value of each expression.
$\sin (2 \cos^{- 1} \frac{4}{5})$

Short Answer

Expert verified

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

Step by step solution

Given information

Given expression $\sin (2 \cos^{- 1} \frac{4}{5})$

Assume θ=cos-1(45) and calculate sine

Calculating, we get

$\sin θ = \sqrt{1 - {(\frac{4}{5})}^{2}} \sin θ = \sqrt{1 - \frac{16}{25}} \sin θ = \sqrt{\frac{9}{25}} \sin θ = \frac{3}{5}$

Substitute values in double angle formula

Using double angle formula, we get

$\sin (2 θ) = 2 \cdot \frac{3}{5} \cdot \frac{4}{5} \sin (2 θ) = \frac{24}{25}$

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In Problems 79-90, find the exact value of each expression.
$\sin (2 \cos^{- 1} \frac{4}{5})$

Short Answer

Step by step solution

Given information

Assume θ=cos-1(45) and calculate sine

Substitute values in double angle formula

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In Problems 79-90, find the exact value of each expression.sin2cos-145

Short Answer

Step by step solution

Given information

Assume θ=cos-1(45) and calculate sine

Substitute values in double angle formula

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

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Study anywhere. Anytime. Across all devices.

In Problems 79-90, find the exact value of each expression.
$\sin (2 \cos^{- 1} \frac{4}{5})$