2 cos 3 theta + 1=0

Question

solve over the interval 0 degrees and 360 degrees

Answer 1

2cos(3θ) + 1 = 0

 

cos(3θ) = -1/2

 

3θ = 120°+k360° or 240°+k360°, where k is any integer

 

So, θ = 40° + k120° or 80° + k120°

 

If k = 0, then θ = 40° or 80°

If k = 1, then θ = 160° or 200°

If k = 2, then θ = 280° or 320°

 

For other values of k, the values of θ are not between 0° and 360° 

Answer 2

cos 3 theta=-1/2

 

3 theta=2 pi/3   OR.  4 pi/3

 

Theta= 2 pi/9   OR.   4 pi/9