use addition identity to find the exact value of sin 75°

Question

use addition identity to find the exact value of sin 75°

Answer 1

sin(75) can be written as    sin(45 + 30).  These angles are values on the unit circle.

 

All you have to do is apply the addition-angle identity formula

 

 

sin(A + B) = sin(A)cos(B) + cos(A)sin(B)

Answer 2

The problem asks you to do sin(30+45) in degrees:  = sin 30 cos 45 + cos 30 sin 45 =

(1/2)(√2)/2+ (√3)/2 (√2)/2 = [√2 + √6]/4

 

Verify by calculator use.