Sum and difference identities

Question

Given cos A=-1/4 where pi/2 <A<pi and sin B=2/3 where pi/2<B<pi,find sin(A+B) and cos(A-B)

Answer 1

Given cos A=-1/4 where pi/2 <A<pi and sin B=2/3 where pi/2<B<pi,find sin(A+B) and cos(A-B)

If CosA = -1/4, we need to find SinA using pythagorean theorem to find the opposite side.

Opposite side = sqrt ( 4^2 - 1^2) = sqrt (15)

So SinA = sqrt(15) / 4

If SinB = 2/3, we need to find CosB the same way.

Adjacent side = sqrt (9 - 4) = sqrt(5) and it will be negative, since it's in the 2nd quadrant.

So CosB = -sqrt(5) / 3

Now fill in the blanks with the Angle Addition Identity. Let me know if you need more guidance!

sin(A+B) = SinA CosB + SinB CosA

Answer 2