# What is the distance between the following polar coordinates?:  (5,(19pi)/12), (3,(11pi)/8)

Apr 16, 2017

$3.130$

#### Explanation:

First, write each polar coordinate as cartesian coordinates. Use the parametric form to write $x$ and $y$:

$x = r \cos \left(\theta\right)$

$y = r \sin \left(\theta\right)$

Plug in for the first point:

$x = 5 \cos \left(19 \frac{\pi}{12}\right) \approx 1.294$

$y = 5 \sin \left(19 \frac{\pi}{12}\right) \approx - 4.830$

Plug in for the second point:

$x = 3 \cos \left(11 \frac{\pi}{8}\right) \approx - 1.148$

$y = 3 \sin \left(11 \frac{\pi}{8}\right) \approx - 2.772$

So we have the two points in the cartesian form: $\left(1.294 , - 4.830\right)$ and $\left(- 1.148 , - 2.772\right)$. Now we can use the distance formula:

d=sqrt((-1.148-1.294)^2+(-2.772-(-4.830))^2~~3.130