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Chapter 7: Q 20. (page 457)

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

csccos-1-32

Short Answer

Expert verified

The value of the expression csccos-1-32=2.

Step by step solution

01

Step 1. Given information.  

The given expression is:

csccos-1-32

Let's take 胃=cos-1-32

cos胃=-32

0鈮�胃鈮�蟺is the domain of the function.

02

Step 2. Find the value of θ.

Initially, we have function cos-1and the bounds of cos function are going to be in the interval role="math" localid="1646466354693" 0,蟺. It represents the range of cos-1.

By using the unit circle, we can say that 胃must be equal to 5蟺6, so that we can get -32.

cos-1胃=-32cos-1-32=5蟺6

03

Step 3. Find the exact value of the expression.

csccos-1-32=csc5蟺6csc胃=1sin胃csc5蟺6=1sin5蟺6

By using the unit circle, we know that sin5蟺6=12

role="math" localid="1646466896004" csc5蟺6=112=2

Therefore,csccos-1-32=2.

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