Question

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

Answer 1

        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