Find the exact value of sinaA ifsin a and sin B 15 and a and

Find the exact value of sin(a-A) ifsin a and sin B 15 and a and B are between 0 and x/2. sin (a-B)

Solution

sin a = 3/5

by pythagorus

perpendicular = 3

hypotnuese = 5

base = root(25-9)

base = 4

cos a = 4/5

sin b = 15/17

perdicular = 15

hypotnuese = 17

base = root(17^2 - 15^2)

base = root ( 64)

base = 8

cos b = 8/17

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

= 3/5 * 8/17 - 4/5* 15/17

=24/ 85 - 60/ 105

= -36 /105