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

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