# What is the polar form of ( -3,-14 )?

Nov 15, 2016

Polar coordinate: $\left(14.3 , 4.5 \text{ radians}\right)$ approx.

#### Explanation:

The point $\left(- 3 , - 14\right)$ is in quadrant 3 (Q III)
with a reference angle of $\theta = \text{arctan} \left(\frac{- 14}{- 3}\right)$
and a radius of r=sqrt(((-3)^2+(-14)^2)

Using a calculator:
$\textcolor{w h i t e}{\text{XXX}} \theta \approx 1.359702994$
$\textcolor{w h i t e}{\text{XXXXXX}}$Note: since this point is in Q III it will be
$\textcolor{w h i t e}{\text{XXXXXX}}$necessary to add $\pi$ to it to get the true
$\textcolor{w h i t e}{\text{XXXXXX}}$polar coordinate angle.
$\textcolor{w h i t e}{\text{XXXXXX}} \theta + \pi \approx 4.501295647$
and
$\textcolor{w h i t e}{\text{XXX}} r \approx 14.31782106$