For which values of theta in the interval 0 degrees<theta<180 degrees is cos 3theta=1

Question

 For which values of Θ in the interval 0°<Θ<180° is cos 3Θ=1

Answer 1

cos 3θ = 1 ... cosine value is 1 for argument 3θ = 0 + k(2pi)

 so

solving for θ we get k (2pi/3) ...

k = 0, θ = 0

k = 1, θ = 2pi/3 = 120^o

k = 2, θ = 4pi/3... but this exceeds 180^o.

 

Since the proposed answer θ is NOT in the interval (0,180), the only solution appears to be 120^o