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Chapter 7: Q. 23 (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.

tansin-1-45

Short Answer

Expert verified

The exact value of the composite function is-43.

Step by step solution

01

Step 1. Given Information 

The given composite function istansin-1-45.

We have to find the exact value.

02

Step 2. Finding the value 

To find the exact value,

Let

x=sin-1-45sinx=-45

The value of sine is negative in the third and fourth quadrant.

The domain of the sine function is -蟺2鈮�x鈮�蟺2.

So,xlies in the fourth quadrant.

03

Step 3. Solve the composite function

Now, to find the value of the composite function we have to find the value oftanx.

So, ifsinx=-45

localid="1646560612002" p=-4,h=5h2=p2+b252=-42+b225-16=b2b=3

Thenlocalid="1646560715756" tanx=-43tansin-1-45=-43

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