Question

What is the distance between the following polar coordinates?: `(1,pi/2), (-1,pi/2)`

Answer 1

There must a mistake, polar coordinates of a point are given in the form `(rho, theta)`, where `rho` is the distance from the origin, and `theta` is the angle formed with the `x`-axis. So, `rho` can't be negative.

If you wanted to know the distance between

`(1,\pi/2)` and `(1,-\pi/2)`,

then you can work like this: since `rho=1`, both points are in the unit circle. And in particular, they are opposite points, since `90^@` and `-90^@` determine the "north pole" and "south pole" of the circle. So, the distance between them is two times the radius, which is `2`.