# How do you convert (6, 6) into polar form?

Jul 6, 2016

Make use of a few formulas to get $\left(6 , 6\right) \to \left(6 \sqrt{2} , \frac{\pi}{4}\right)$.

#### Explanation:

The desired conversion from $\left(x , y\right) \to \left(r , \theta\right)$ can be accomplished with the use of the following formulas:
$r = \sqrt{{x}^{2} + {y}^{2}}$
$\theta = {\tan}^{- 1} \left(\frac{y}{x}\right)$

Using these formulas, we obtain:
$r = \sqrt{{\left(6\right)}^{2} + {\left(6\right)}^{2}} = \sqrt{72} = 6 \sqrt{2}$
$\theta = {\tan}^{- 1} \left(\frac{6}{6}\right) = {\tan}^{- 1} 1 = \frac{\pi}{4}$

Thus $\left(6 , 6\right)$ in rectangular coordinates corresponds to $\left(6 \sqrt{2} , \frac{\pi}{4}\right)$ in polar coordinates.