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