# What is the distance between the following polar coordinates?:  (3,(-4pi)/3), (4,(-5pi)/6)

Apr 16, 2017

$5$

#### Explanation:

First, write the polar coordinates in cartesian form. You will need the parametric form to help you with that:

$x = r \cos \theta$

$y = r \sin \theta$

Plug in for the first point:

$x = 3 \cos \left(- 4 \frac{\pi}{3}\right) = - 1.5$

$y = 3 \sin \left(- 4 \frac{\pi}{3}\right) = \frac{3 \sqrt{3}}{2}$

Plug in for the second point:

$x = 4 \cos \left(- 5 \frac{\pi}{6}\right) = - 2 \sqrt{3}$

$y = 4 \sin \left(- 5 \frac{\pi}{6}\right) = - 2$

So now we have the two points: (-1.5,3sqrt3)/2) and $\left(- 2 \sqrt{3} , - 2\right)$. Now use the distance formula:

d=sqrt((-2sqrt(3)-(-1.5))^2+ (-2-(3sqrt3)/2)^2=5