# What is the distance between the following polar coordinates?:  (1,(-5pi)/12), (3,(pi)/8)

Apr 15, 2017

$3.284$

#### Explanation:

Write each polar point as a cartesian point using parametric equations.

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

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

For $\left(1 , - 5 \frac{\pi}{12}\right)$

$x \left(t\right) = 1 \cos \left(- 5 \frac{\pi}{12}\right) \approx .259$

$y \left(t\right) = 1 \sin \left(- 5 \frac{\pi}{12}\right) \approx - .966$

For $\left(3 , \frac{\pi}{8}\right)$

$x = 3 \cos \left(\frac{\pi}{8}\right) \approx 2.772$

$y = 3 \sin \left(\frac{\pi}{8}\right) \approx 1.148$

So now we have the points in cartesian form:

$\left(.259 , - .966\right) , \left(2.772 , 1.148\right)$

Use distance formula:

$d = \sqrt{{\left(2.772 - .259\right)}^{2} + {\left(1.148 - \left(- .966\right)\right)}^{2}} \approx 3.284$