Find the exact value of the trigonometric expression given that sin(u) = − 3/5 , where 3𝜋/2 < u < 2𝜋, and cos(v) = 15/17 , where 0 < v < 𝜋/2. cos(u − v)

Answer 1

cos(u-v) = cos(u)cos(v) + sin(u)sin(v)

Need to find cos(u) and sin(v) first.

If sin(u) = -3/5 in the 4th quadrant, this is a 3-4-5 triangle, so cos(u) = 4/5.

If cos(v) = 15/17 in the 1st quadrant, this is a 8-15-17 triangle, so sin(v) = 8/17.

cos(u-v) = (4/5)(15/17) + (-3/5)(8/17) = (60 - 24)/(5•17) = 36/85