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Chapter 7: Q 21. (page 457)

In Problems 9鈥�36, find the exact value of each expression.

cos-1sin5蟺4

Short Answer

Expert verified

The value of the expressioncos-1sin5蟺4=3蟺4.

Step by step solution

01

Step 1. Write the given information.  

The given expression is:

cos-1sin5蟺4

02

Use the trigonometric identities. 

Use the identity sin蟺2+x=cosx,

cos-1sin5蟺4=cos-1sin蟺2+3蟺4=cos-1cos3蟺4

03

Use the identity cos-1cos x=x.

cos-1cos3蟺4=3蟺4

Therefore,cos-1sin5蟺4=3蟺4.

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