# What is the distance between the following polar coordinates?:  (5,(7pi)/4), (9,(11pi)/8)

Jul 9, 2018

color(violet)("Distance " d ~~ 8.4592

#### 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)

$\text{Given } {r}_{1} = 5 , {r}_{2} = 9 , {\theta}_{1} = {\left(\frac{7 \pi}{4}\right)}^{c} , {\theta}_{2} = {\left(\frac{11 \pi}{8}\right)}^{c}$

d = sqrt (5^2 + 9^2 - (2 * 5 * 9 * cos ((11pi)/8 - (7pi)/4))

color(violet)(d )= sqrt (106 - 90 cos ((-3pi)/8)) color(violet)(~~ 8.4592