Question

Given sin a=−2/5 and cos b=1/3 with a and b both in the interval (3π/2,2π), find sin(a+b)

Answer 1

`-(8√(2)+2)/(15).`

Explanation:

1) sin(a+b)=sin(a)cos(b)+sin(b)cos(a);

2) if sin(a)=-0.4, then cos(a)=0.8; if cos(b)=1/3, then sin(b)=-√8/3;

3) finally, sin(a+b)=-0.4*1/3-√8/3*0.8=

`=-(8√(2)+2)/(15).`