# What is the distance between polar coordinates (-2, 300^circ) and (2, 10^circ)?

Jul 9, 2018

color(indigo)("Distance " d ~~ 3.2766

#### Explanation:

$d = \sqrt{{r}_{1}^{2} + {r}_{2}^{2} - 2 {r}_{1} {r}_{2} \cos \left({\theta}_{1} - {\theta}_{2}\right)}$

$\left({r}_{1} , {\theta}_{1}\right) = \left(- 2 , {300}^{\circ}\right) , \left({r}_{2} , {\theta}_{2}\right) = \left(2 , {10}^{\circ}\right)$

d = sqrt(-2^2 + 2^2 - 2 * -2 * 2 * cos (300-10)

$d = \sqrt{8 + 8 \cos 290} \approx 3.2766$