Show that (cosθ + sinθ) may be written in the form rsin(θ+t). Determine the value of r and a. hence or otherwise Solve 3cosθ+4sinθ = 4completely

Determine the value of r and a. hence or otherwise
Solve 3cosθ+4sinθ = 4completely
Solution
Compare cosθ + sinθ
3cosθ+4sinθ
= 3, = 4

R = 5
Tan = a/b = ¾ = 0.75
Tan
Tan-1(0.75)
= 36.9

3cosθ+4sinθ = Rsin(θ+)
4 = Rsin(θ+36.9⁰)
4 = 5sin(θ+36.9⁰)
4/5 = sin(θ+36.9⁰)
0.8 = sin(θ+36.9⁰)
θ+36.9 = sin-1(0.8)
θ+36.9 = 53.9
θ = 53.9 – 36.9
θ = 16.20