# How do you convert (theta) = pi/3 into cartesian form?

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Nov 28, 2015

$y = \sqrt{3} x$

#### Explanation:

There are several equalities used to convert between rectangular and polar coordinates. For a list and good explanation as to why they work, see How do you convert rectangular coordinates to polar coordinates?

In this case, as we have no $r$ to consider, we will only need

$\frac{y}{x} = \tan \left(\theta\right)$

Multiplying both sides by $x$ gives

$y = \tan \left(\theta\right) x$

But substituting $\theta = \frac{\pi}{3}$ we get

$y = \tan \left(\frac{\pi}{3}\right) x$

$\implies y = \sqrt{3} x$

(Note that this is as expected, as the polar plot $\theta = \frac{\pi}{3}$ takes on all $r$ values for the angle $\frac{\pi}{3}$, forming a straight line)

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