# What is the distance between the following polar coordinates?:  (2,(pi)/4), (3,(13pi)/8)

May 16, 2016

$d = 4.90781$

#### Explanation:

First we pass the points in polar coordinates to Cartesian. The pass equations are
$x = r \cos \left(\theta\right)$
$y = r \sin \left(\theta\right)$
$\left(2 , \frac{\pi}{2}\right) \to \left(2 \cos \left(\frac{\pi}{2}\right) , 2 \sin \left(\frac{\pi}{2}\right)\right) = \left(0 , 2\right) = \left({x}_{1} , {y}_{1}\right)$
$\left(3 , \frac{13 \pi}{8}\right) \to \left(3 \cos \left(\frac{13 \pi}{8}\right) , 3 \sin \left(\frac{13 \pi}{8}\right)\right) = \left(1.14805 , - 2.77164\right) = \left({x}_{2} , {y}_{2}\right)$
Now we calculate the distance d = sqrt((x_1-x_2)^2+(y_1-y_2)²) = 4.90781