Question

suppose sin(x)=4/5 and cos(y)=-12/13, and x and y are in the second quadrant. determine the value of each expression: sin(x+y), cos(x-y), cos2x, sin2y.

Answer 1

you should recognize the 3,4,5 and the 5,12, 13 right-angled triangles, so

if sinx = 4/5, then cosx = -3/5 in II
if cosy = -1213, then siny = 5/13 in II

to have this type of question, you must also have come across the expansions for sin(A+B), cos(A-B), etc.

I will do cos(x-y)

cos(x-y) = cosx cosy + sinx siny
= (-3/5)(-12/13) + (4/5)(5/13)
= 56/65