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 :-/

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- Jun 10th 2012, 10:38 AMDeeRoseSolve the equation of Cos3(theta) = 1/2
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 :-/ - Jun 10th 2012, 10:51 AMGokuRe: Solve the equation of Cos3(theta) = 1/2
$\displaystyle cos(3\theta) = \frac{1}{2}$

$\displaystyle 3\theta = cos^{-1}(\frac{1}{2})$

$\displaystyle 3\theta =60 $ degrees

$\displaystyle \theta = 20$ degrees $\displaystyle + 360k $ where k is any integer. - Jun 10th 2012, 10:52 AMReckonerRe: Solve the equation of Cos3(theta) = 1/2
- Jun 10th 2012, 10:53 AMReckonerRe: Solve the equation of Cos3(theta) = 1/2
- Jun 10th 2012, 11:20 AMDeeRoseRe: Solve the equation of Cos3(theta) = 1/2
It's Cos3(theta) ..Not Cos

**^**3(theta) Is Goku's response the right one then? - Jun 10th 2012, 11:30 AMReckonerRe: Solve the equation of Cos3(theta) = 1/2
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 $\displaystyle k\in\mathbb{Z}$. - Jun 10th 2012, 12:22 PMDeeRoseRe: Solve the equation of Cos3(theta) = 1/2
Thanks alot! :-)