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Chapter 7: Q. 10 (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-1cos3蟺4

Short Answer

Expert verified

The exact value is3蟺4.

Step by step solution

01

Step 1. Given Information

We are given a composite function cos-1cos3蟺4.

We need to find its exact value.

02

Step 2. Concept used

The cosine function and its inverse, form these properties

cos-1(cosx)=xwhere0鈮�x鈮�蟺

and

cos(cos-1x)=xwhere-1鈮�x鈮�1

03

Step 3. Find the exact value

As 3蟺4lies in the interval 0,蟺. So using the property formed by cosine and its inverse function we have

cos-1cos3蟺4=3蟺4

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