Question

What is the distance between the following polar coordinates?: `(3,(-7pi)/12), (2,(7pi)/8)`

Answer 1

`sqrt(13-12cos((35pi)/24)) approx 3.81658411497`

Explanation:

Say you have two polar coordinates `(r_1, theta_1)` and `(r_2, theta_2)`. In this case make a triangle with vertices at the origin and each point. Around the vertex of the origin we have two sides of lengths `r_1` and `r_2`, and we have angle `|theta_1 - theta_2|`. By the law of cosines, the third side is `sqrt(r_1^2+r_2^2-2r_1r_2cos(theta_1-theta_2))`

To find our distance we just then have:

`sqrt(13-12cos((35pi)/24)) approx 3.81658411497`