# What is the distance between the following polar coordinates?:  (4,(-19pi)/12), (2,(-3pi)/8)

Apr 10, 2018

Distance between points is $5.72$ unit

#### Explanation:

Polar coordinates of point A is ${r}_{1} = 4 , {\theta}_{1} = \frac{- 19 \pi}{12}$

Polar coordinates of point B is ${r}_{2} = 2 , {\theta}_{2} = \frac{- 3 \pi}{8}$

Distance between points $A \mathmr{and} B$ is

D= sqrt(r_1^2+r_2^2-2r_1r_2cos(theta1-theta2) or

$D = \sqrt{\left(16 + 4 - 16 \cdot \cos \left(\frac{- 19 \pi}{12} - \frac{- 3 \pi}{8}\right)\right)} \approx 5.72$ unit

Distance between points is $5.72$ unit [Ans]