# What is the polar form of ( 11,-9 )?

Mar 22, 2018

The polar form of the coordinate pair $\left(11 , - 9\right)$ is $\left(\sqrt{202} , - 39.289\right)$.

#### Explanation:

The polar form of a coordinate pair $\left(x , y\right)$ is $\left(r , \theta\right)$.
To find r, we use the formula ${r}^{2} = {x}^{2} + {y}^{2}$.
${r}^{2} = {11}^{2} + {\left(- 9\right)}^{2}$
${r}^{2} = 121 + 81$
${r}^{2} = 202$
$r = \sqrt{202}$
$r \approx 14.21$
To find $\theta$, we use the formula $\frac{y}{x} = \tan \left(\theta\right)$.
$\frac{- 9}{11} = \tan \left(\theta\right)$
$\theta = {\tan}^{-} 1 \left(\frac{- 9}{11}\right)$
$\theta \approx {\tan}^{-} 1 \left(0.818182\right)$
$\theta \approx - 39.289407$