# What is the polar form of ( -7,-1 )?

Jul 6, 2017

$\left(\sqrt{50} , 3.28\right)$

#### Explanation:

To convert this to a polar coordinate $\left(r , \theta\right)$, you can use the following formulas and substitute $- 7$ for $x$ and $- 1$ for $y$.

${r}^{2} = {x}^{2} + {y}^{2}$
$\tan \theta = \frac{y}{x}$

${r}^{2} = {\left(- 7\right)}^{2} + {\left(- 1\right)}^{2}$
${r}^{2} = 49 + 1$
${r}^{2} = 50$
$r = \sqrt{50}$

$\tan \theta = \frac{y}{x}$
$\tan \theta = \frac{- 1}{- 7}$
$\theta = {\tan}^{-} 1 \left(\frac{1}{7}\right)$
$\theta \approx 0.14$

Since the coordinate is in quadrant $\text{III}$, we must add $\pi$ to this for the correct angle:

$= 0.14 + \pi \approx 3.28$

Thus, the polar form of $\left(- 7 , - 1\right)$ is $\left(\sqrt{50} , 3.28\right)$.

Jul 6, 2017

$\left(\sqrt{50} , 3.283\right)$ (in radians)

#### Explanation:

The polar form of a rectangular coordinate is given by

$r = \sqrt{{x}^{2} + {y}^{2}}$

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

So,

r = sqrt((-7)^2 + (-1)^2) = color(red)(sqrt(50)

$\theta = \arctan \left(\frac{- 1}{- 7}\right) = 0.142$ $\text{rad}$ + pi = color(blue)(3.283 color(blue)("rad"

$\pi$ was added because the coordinate is in the third quadrant.

The polar form is thus

$\left(\textcolor{red}{\sqrt{50}} , \textcolor{b l u e}{3.283}\right)$