Find the exact value under the given conditions sin alpha 3

Find the exact value under the given conditions. sin alpha = 3/5, pi/2

Solution

we have given sin=3/5,pi/2<<pi, and cos=15/17,0<<pi/2

cos=sqrt(1-sin²) =sqrt(1-9/25)=sqrt(16/25)=4/5

sin=sqrt(1-cos²)=sqrt(1-225/289)=sqrt(64/289)=8/17

sin(-)=sincos-cossin

sin(-)=3/5*15/17-4/5*8/17

=45/85-32/85=13/85

sin(-)=13/85

answer is 3) 13/85