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