# What is the distance between the following polar coordinates?:  (2,(12pi)/8), (1,(-pi)/8)

##### 1 Answer
Jul 9, 2018

color(purple)("Distance between the two polar coordinates " d )color(purple)(~~ 1.8626

#### Explanation:

Distance between tow points knowing the polar coordinates is given by the formula using cosine rule

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

$\text{Given } {r}_{1} = 2 , {r}_{2} = 1 , {\theta}_{1} = {\left(\frac{12 \pi}{8}\right)}^{c} , {\theta}_{2} = {\left(- \frac{\pi}{8}\right)}^{c}$

d = sqrt (2^2 + 1^2 - (2 * 2 * 1 * cos (-pi/8 - (12pi)/8))

color(purple)(d )= sqrt (5 - 4 cos ((-13pi)/8)) color(purple)(~~ 1.8626