Question

Angle x is in the second quadrant and angle y is in the first quadrant such that sinx=5/13 and cosy=3/5, determine and exact value for cos (x+y).
I have no idea how to even start this question. Could someone please help me?

Answer 1

x=arcsin(5/13)
y=arccos(3/5)

so find those calculations and plug it into cos(x+y) or in other words
cos(x+y)=(arcsin(5/13)+arccos(3/5))

Answer 2

Well, I understand what you mean by the solution, but I am getting a really long decimal as the answer, so that's not an excat value. Please, can you help me some more?

Answer 3

Make diagrams of your triangles in the corresponding quadrants

if sinx = 5/13 and is in II
then cosx = -12/13

if cosy = 3/5 and is in I
then siny = 4/5

cos(x+y) = cosxcosy - sinxsiny
= (-12/13)(3/5) - (5/13)(4/5)
= -56/65