Question

What is the distance between the following polar coordinates?: `(2,(9pi)/4), (14,(-3pi)/8)`

Answer 1

The distance `~~ 14.88`

Explanation:

When given two polar points `(r_1,theta_1)` and `(r_2,theta_2)`, the distance between the two points can be found using a variant of the the Law of Cosines:

`d = sqrt(r_1^2+r_2^2-2(r_1)(r_2)cos(theta_2-theta_1)`

We are given: `r_1 = 2, theta_1 = (9pi)/4, r_2 = 14, and theta_2 = (-3pi)/8`

`d = sqrt(2^2+14^2-2(2)(14)cos((-3pi)/8-(9pi)/4)`

`d~~14.88`