Solve the equation of Cos3(theta) = 1/2 , for theta is an element of real numbers, where (theta) is in radius.
I feel like it's simple but I don't know how :-/
$\displaystyle cos(3\theta) = \frac{1}{2}$
$\displaystyle 3\theta = cos^{-1}(\frac{1}{2})$
$\displaystyle 3\theta =60 $ degrees
$\displaystyle \theta = 20$ degrees $\displaystyle + 360k $ where k is any integer.
Note that cosine is equal to $\displaystyle \frac12$ for any angle that is coterminal with $\displaystyle \frac\pi3$ or $\displaystyle -\frac\pi3$. Thus
$\displaystyle \cos3\theta=\frac12$
$\displaystyle \Rightarrow3\theta = 2k\pi\pm\frac\pi3$
$\displaystyle = \frac{(6k\pm1)\pi}3$
$\displaystyle \Rightarrow\theta = \frac{(6k\pm1)\pi}9$
where $\displaystyle k\in\mathbb{Z}$.