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Chapter 7: Q. 9 (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.

sin-1sin3蟺8

Short Answer

Expert verified

The exact value is3蟺8.

Step by step solution

01

Step 1. Given Information

We are given a composite functionsin-1sin3蟺8.

We need to find its exact value.

02

Step 2. Concept used

The sine function and its inverse, form these properties

sin-1(sinx)=xwhere-蟺2鈮�x鈮�蟺2

and

sin(sin-1x)=xwhere-1鈮�x鈮�1

03

Step 3. Find the exact value

As 3蟺8lies in the interval -蟺2,蟺2. So using the property formed by sine and its inverse function we have

sin-1sin3蟺8=3蟺8

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