Trig functions

Question

cos(3theta)=-1

solve for exact solutions over the interval [0,360 degrees]

 

I am having trouble finding a place to start.

Answer 1

cos(3θ) = -1

 

     3θ = 180° + (360°k, where k = 0, ±1, ±2, ±3, ...

 

       θ = 60° + (120°)k

 

If k = 0, then θ = 60°

If k = 1, then θ = 180°

If k = 2, then θ = 300°

 

Other choices of k give values of θ that are outside of the interval [0°, 360°].

 

Solutions:  60°, 180°, 300°