Question

Given Sin(A) = 3/5 and Cos(B) = 8/17 in Quad 1, what is the Quadrant of A+B?

Answer 1

So far I have:
Sin(a + b) = 84/85, and cos(a + b) = -13/85, and also tan(a + b) = -6.46

Answer 2

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

cos² a = 1 - sin² a = 1 - 9/25 = 16/25

<=>

cos a = -4/5 (quadran 2)


sin² b = 1 - cos² b = 1 - 64/289 = 225/289

<=>

sin b = 15/17


sin (a - b) = 3/5 * (-8/17) - 15/17 * (-4/5) = -24/85 + 60/85 =

36/85


cos (2b) = cos² b - sin² b = 64/289 - 225/289 = -161/289