2Cos3Θ = 1?

Question

Solve For Θ

0 ≤ Θ < 360

Answer 1

2cos(3θ) = 1
cos(3θ) = 1/2

let u = 3θ

0 ≤ θ < 360
3(0) ≤ 3θ < 3(360)
0 ≤ u < 1080

Then
cos(u) = 1/2,
u = π/3, 5π/3, 7π//3, 11π/3, 13π/3, 17π//3

So
3θ = π/3, 5π/3, 7π//3, 11π/3, 13π/3, 17π//3

Divide both sides by 3:
θ = π/9, 5π/9, 7π//9, 11π/9, 13π/9, 17π//9

Answer 2

cos 3 t = 1/2 so 3t = 60 +k*360 degrees and -60+k*360
t= 20+k*120 degrees and -20+k*120
so t = 20,140 , 260 deg and 100,220 and 340.
There are six solutions

Answer 3

2Cos3Θ=1
Cos3Θ=1/2
Θ=1/3 x Arccos(1/2)