# Thread: Solve the equation of Cos3(theta) = 1/2

1. ## Solve 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 :-/

2. ## Re: 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.

3. ## Re: Solve the equation of Cos3(theta) = 1/2

Originally Posted by DeeRose
Solve the equation of Cos3(theta) = 1/2 , for theta is an element of real numbers, where (theta) is in radius.
Is this supposed to be $\displaystyle \cos3\theta=\frac12$ or $\displaystyle \cos^3\theta = \frac12\mathrm?$ If the latter, are you looking for an exact solution?

4. ## Re: Solve the equation of Cos3(theta) = 1/2

Originally Posted by Goku
$\displaystyle \theta = 20$ degrees
Your procedure is good, but this is only one of infinitely many solutions.

5. ## Re: Solve the equation of Cos3(theta) = 1/2

It's Cos3(theta) ..Not Cos^3(theta) Is Goku's response the right one then?

6. ## Re: Solve the equation of Cos3(theta) = 1/2

Originally Posted by DeeRose
It's Cos3(theta) .. Is Goku's response the right one then?
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 $\displaystyle k\in\mathbb{Z}$.

7. ## Re: Solve the equation of Cos3(theta) = 1/2

Thanks alot! :-)

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# 1/2 cos 3theta =?

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