# What is the distance between the following polar coordinates?:  (7,(19pi)/12), (4,(13pi)/8)

Jul 9, 2018

color(blue)(" Distance bet. the polar coordinates " d ~~ 3.0788

#### Explanation:

Distance between two 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)

$\text{Given } {r}_{1} = 7 , {r}_{2} = 4 , {\theta}_{1} = {\left(\frac{19 \pi}{12}\right)}^{c} , {\theta}_{2} = {\left(\frac{13 \pi}{8}\right)}^{c}$

d = sqrt (7^2 +4^2 - (2 * 7 * 4* cos ((13pi)/8 - (19pi)/12))

$\textcolor{b l u e}{d} = \sqrt{65 - 56 \cos \left(\frac{\pi}{24}\right)} \textcolor{b l u e}{\approx 3.0788}$