Question

find sin(alpha-beta) if sin alpha =-5/13 with alpha between pi and 3pi/2; cos beta=2/5 with beta between 3pi/2 and 2pi

Answer 1

sin(α) = ⁻⁵/₁₃
sin⁻¹[sin(α)] = sin⁻¹(⁻⁵/₁₃)
α ≈ 1.1256π

cos(β) = ²/₅
cos⁻¹[cos(β)] = cos⁻¹(²/₅)
β ≈ 1.6311π

sin(α - β) = sin(1.1256π - 1.6311π)
sin(α - β) = sin(-0.5055π)
sin(α - β) = -sin(0.5055π)
sin(α - β) = -sin(90.99)
sin(α - β) ≈ -0.116