Evaluate the expression given that cosine a=4/5 with 0<a<pi/2 and sin b=-15/17 with 3pi/2< b<2pi

Answer 1

cos a = 4/5, and a is in quad I
Make your sketch and use Pythagoras:
x^2 + y^2 = r^2
16 + y^2 = 25
y^2 = 9
y = 3 in quad I
so sin a = 3/5

do the same for sin b = -15/17 , b in quad IV
x^2 + 225 = 289
x = +8 in quad IV

evaluate WHAT expression ?
but you now have both sines and cosines of both angles.