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Chapter 7: Q. 24 (page 495)

In Problems 19鈥�28, use the Half-angle Formulas to find the exact value of each expression.

sin195掳

Short Answer

Expert verified

The exact value of the expression sin195掳by using Half angle formula is -2-32

Step by step solution

01

Step 1. Given

An expressionsin195掳

To find the exact value of the expression

02

Step 2. Half angle formula

The half angle formula is,

sin胃2=卤1-cos胃2

03

Step 3. Consider an angle

Consider an angle,

sin胃=sin390掳胃=390掳胃2=390掳2=195掳

04

Step 4. Use the half-angle formula

By Half-angle formula,

sin195掳=卤1-cos390掳2

We know that,

cos390掳=cos(360掳+30掳)=cos30掳=32

05

Step 5. Substitute the values

Substitute the values in the above formula,

sin195掳=卤1-322=卤2-322=卤2-34=卤2-32

06

Step 6. Find the exact value.

Since 195掳lies in the third quadrant,

sin195掳=-2-32

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