# What is the polar form of ( -18,-6 )?

Jun 27, 2017

$\left(18.974 , 3.463\right)$

#### Explanation:

We're asked to find the polar form of a rectangular coordinate.

We can do so by using the equations

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

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

The $x$-coordinate is $- 18$, and the $y$-coordinate is $- 6$, so

r = sqrt((-18)^2 + (-6)^2) = color(red)(18.974

theta = arctan((-6)/(-18)) = 0.322 + pi = color(blue)(3.463

The $\pi$ was added to fix the calculator error, the coordinate is located in quadrant $I I I$. (Remember the angle $\theta$ is in radians.)

The polar form of this coordinate is thus

$\left(\textcolor{red}{18.974} , \textcolor{b l u e}{3.463}\right)$