Question

What is the distance between the following polar coordinates?: `(16,(19pi)/12), (11,(17pi)/8)`

Answer 1

Distance between the polar coordinates is `20.566`

Explanation:

A polar coordinate `(r,theta)` is `(rcostheta,rsintheta)` in Caresian coordinates.

Hence `(16,(19pi)/12)` is `(16cos(19pi)/12,16sin(19pi)/12)` or `(16xx0.2588,16xx-0.9659)` or `(4.1408,-15.4544)`

`(11,(17pi)/8)` is `(11cos(17pi)/8,11sin(7pi)/8)` or `(11xx0.9239,11xx0.3827)` or `(10.1629,4.2097)`

Hence distance between two points is given by `sqrt((10.1629-4.1408)^2+(4.2097+15.4544)^2)` or

`sqrt(6.0221^2+19.6641^2)`

= `sqrt(36.2657+386.6768)`

= `sqrt422.9425=20.566`