Use the sum or the difference identity for the sure function

Use the sum or the difference identity for the sure function to evaluate exn sup expression exactly (a) sin(5 pi/1_2) (b) sin 75 degree Find exact value op sin (a - beta) if since a = -3/5 and sin beta = 1/5 and the terminal side of as lies in the quadrant in and the terminal side of beta lies in quadrant 1. Find sin x = -4/5 cos x

Solution

4. a. sin(5pi/12) = sin(pi/4 +pi/6)

sin pi/4 cos pi/6+cos pi/4 sin pi/6

=(sqrt2/2)(sqrt3/2)+(sqrt2/2)(1/2)

(sqrt2/4)(sqrt3+1)

b. sin 75= sin(45+30)

sin 45 cos 30+cos 45 sin 30

(sqrt2/2)(sqrt3/2)+(sqrt2/2)(1/2)

(sqrt2/4)(sqrt3+1)

5. sin a=-3/5

cos a=-4/5

sin b =1/5

cos b= 2sqrt6/5

sin(a-b)=sin a cos b- cos a sin b

= (-3/5)(2sqrt6/5)-(-4/5)(1/5)

=(-6sqrt6 +4)/25