Chapter 7: Q 21. (page 457)

In Problems 9–36, find the exact value of each expression.
$\cos^{- 1} (\sin \frac{5 π}{4})$

Short Answer

Expert verified

The value of the expression $\cos^{- 1} (\sin \frac{5 π}{4}) = \frac{3 π}{4}$ .

Step by step solution

Step 1. Write the given information.

The given expression is:

$\cos^{- 1} (\sin \frac{5 π}{4})$

Use the trigonometric identities.

Use the identity $\sin (\frac{π}{2} + x) = \cos x$ ,

$\cos^{- 1} (\sin \frac{5 π}{4}) = \cos^{- 1} [\sin (\frac{π}{2} + \frac{3 π}{4})] = \cos^{- 1} [\cos (\frac{3 π}{4})]$

Use the identity cos-1cos x=x.

$\cos^{- 1} [\cos (\frac{3 π}{4})] = \frac{3 π}{4}$

Therefore, $\cos^{- 1} (\sin \frac{5 π}{4}) = \frac{3 π}{4}$ .

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In Problems 9–36, find the exact value of each expression.
$\cos^{- 1} (\sin \frac{5 π}{4})$

Short Answer

Step by step solution

Step 1. Write the given information.

Use the trigonometric identities.

Use the identity cos-1cos x=x.

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In Problems 9–36, find the exact value of each expression.cos-1sin5π4

Short Answer

Step by step solution

Step 1. Write the given information.

Use the trigonometric identities.

Use the identity cos-1cos x=x.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Logic and Functions

Pure Maths

Probability and Statistics

Decision Maths

Geometry

Study anywhere. Anytime. Across all devices.

In Problems 9–36, find the exact value of each expression.
$\cos^{- 1} (\sin \frac{5 π}{4})$