ANSWER
EXPLANATION
The given trigonometric equation is:
[tex]2 \cos( \theta) - 1 = 0[/tex]
[tex] \implies \: 2 \cos( \theta) = 1[/tex]
[tex]\implies \: \cos( \theta) = \frac{1}{2} [/tex]
The cosine ratio is positive in the first and fourth quadrants.
In the first quadrant,
[tex]\theta = \cos ^{ - 1} ( \frac{1}{2}) [/tex]
[tex]\theta = \frac{\pi}{3} [/tex]
In the fourth quadrant,
[tex]\theta =2 \pi - \cos ^{ - 1} ( \frac{1}{2}) [/tex]
[tex]\theta =2 \pi - \frac{\pi}{3} [/tex]
[tex]\theta = \frac{5\pi}{3} [/tex]
Therefore on the interval, [0,2π] the solution to the given trigonometric equation is:
[tex]\theta = \frac{\pi}{3} \: and \: \frac{5\pi}{3} [/tex]
