Find the exact value for the expression under the given conditions. (cosα+β), sinα = −3/ 5 for α in Quadrant III and cosβ = −3/4 for β in Quadrant II.

Answer 1

cos(α+β)=cos(α)cos(β)-sin(α)sin(β)

If sin(α)=-3/5 in QIII then cos(α)=-4/5 (3-4-5 triangle)

if cos(β) = -3/4 in QII then sin(β) = +√(16-9)/4=√7/4

cos(α+β)=cos(α)cos(β)-sin(α)sin(β) =(-4/5)(-3/4)-(-3/5)(√7/4)

= 12/20+3√7/20 = (12+3√7)/20 ≈ 0.9969