If sin x = 1/3 and sec y = 5/4 where x and y lie between 0 and pi/2, evaluate sin (x-y)

sin (x) = ¹/₃

sin⁻¹[sin (x) ] = sin⁻¹ (¹/₃)

x ≈ 0.34°

x = ¹⁷/₉₀₀₀π

sec (y) = 1¹/₄

1 = 1¹/₄cos (y)

⁴/₅ = cos (y)

cos⁻¹ (⁴/₅) = cos⁻¹[cos (y) ]

0.64 ≈ y

⁴/₁₁₂₅π = y

sin (x - y) = sin (¹⁷/₉₀₀₀π - ⁴/₁₁₂₅π)

sin (x - y) = sin (⁻¹/₆₀₀π)

sin (x - y) = - sin (¹/₆₀₀π)

sin (x - y) = - sin (³/₁₀)

sin (x - y) ≈ - 0.3