Question

Diketahui sin A = 3/5 dan cos B = 15/17, dengan A dan B sudut lancip . tentukan nilai dari sin (A+B) dan cos (A-B)

Answer 1

Sin A = y/r = 3/5
y = 3
r = 5
maka didapat x = 4
  cos A = x/r = 4/5

cos B = x/r = 15/17
x = 15
r = 17
maka didapat y = 8
  sin B = y/r = 8/17

sin(A+B) = sinAcosB + cosAsinB
              = 3/5 x 15/17 + 4/5 x 8/17
              = 9/17 + 32/85
              = 77/85
cos(A-B) = cosAcosB + sinAsinB
              = 4/5 x 15/17 + 3/5 x 8/17
              = 12/17 + 24/85
              = 84/85