# What is the distance between the following polar coordinates?:  (2,(9pi)/4), (14,(-3pi)/8)

Jun 20, 2017

The distance $\approx 14.88$

#### Explanation:

When given two polar points $\left({r}_{1} , {\theta}_{1}\right)$ and $\left({r}_{2} , {\theta}_{2}\right)$, the distance between the two points can be found using a variant of the the Law of Cosines:

d = sqrt(r_1^2+r_2^2-2(r_1)(r_2)cos(theta_2-theta_1)

We are given: ${r}_{1} = 2 , {\theta}_{1} = \frac{9 \pi}{4} , {r}_{2} = 14 , \mathmr{and} {\theta}_{2} = \frac{- 3 \pi}{8}$

d = sqrt(2^2+14^2-2(2)(14)cos((-3pi)/8-(9pi)/4)

$d \approx 14.88$