# How do you convert x=2 into polar form?

Jul 29, 2016

I found: $r = \frac{2}{\cos} \left(\theta\right)$

#### Explanation:

Consider the "conversion" diagram between Cartesian and Polar:

$\text{POLAR"->"CARTESIAN}$
You can see that from Pythagoras: $r = \sqrt{{x}^{2} + {y}^{2}}$ and from Trigonometry: $\theta = \arctan \left(\frac{y}{x}\right)$.

OR

$\text{CARTESIAN"->"POLAR}$
From rigonometry:
$x = r \cos \left(\theta\right)$
$y = r \sin \left(\theta\right)$

Let us consider our expression:
$x = 2$
let us use our second transformation formulas in the form: $x = r \cos \left(\theta\right)$
to get:
$r \cos \left(\theta\right) = 2$
and:
$r = \frac{2}{\cos} \left(\theta\right)$