Question

What is the distance between the following polar coordinates?: `(2,(23pi)/12), (3,(7pi)/8)`

Answer 1

The distance is `~~ 4.9897`

Explanation:

Let's begin by rotating both points an additional `pi/12`, because that will make the first point go around a full rotation and its angle will be zero:

`(2, 0), (3, (23pi)/24)`

These points form a triangle with the origin.

side `a = 2`

side `b = 3`

The `angle C" between the sides" = (23pi)/24`

We can use the Law of Cosines to find the length of side c, which is, also, the distance between the two points:

`c = sqrt(a^2 + b^2 - 2(a)(b)cos(C)`

`c = sqrt(2^2 + 3^2 - 2(2)(3)cos((23pi)/24)`

`c ~~ 4.9897`