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Chapter 7: Q. 19 (page 503)

In Problems 9鈥�23, find the exact value, if any, of each composite function. If there is no value, say it is 鈥渘ot defined.鈥� Do not use a calculator.

cos-1tan3蟺4

Short Answer

Expert verified

The exact value of the composite function is蟺.

Step by step solution

01

Step 1. Given Information 

The given composite function iscos-1tan3蟺4.

We have to find the exact value.

02

Step 2. Finding the value 

To find the exact value, let

x=tan3蟺4x=tan蟺-蟺4x=-tan蟺4tan蟺-胃=-tan胃

The value of tan蟺4=1, x=-1

03

Step 3. Solve the composite fuction 

Now, substitute thexvalue in the given function.

Thus,

cos-1tan3蟺4=cos-1-1=cos-1肠辞蝉蟺肠辞蝉蟺=-1

By using the properties of an inverse function, ff-1x=coscos-1x=xwhere-1鈮�x鈮�1

So,cos-1肠辞蝉蟺=蟺

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