Question

What is the polar form of `( -5,-1 )`?

Answer 1

`(sqrt26,arctan(1/5) - pi)`

Explanation:

Let `A(-5,-1)`.The polar form will be something like `(r,theta)` with r non-negative and `theta in [0,2pi]`.

The module will be given by the norm of the vector `OA` which is `sqrt((-5)^2 + (-1)^2) = sqrt26`.

The angle between the `(Ox)` axis and the vector `OA` will be given by `arctan(y/x) - pi = arctan((-1)/(-5)) - pi = arctan(1/5) - pi` (we substract `pi` because `x < 0` and `y < 0`, and it will give us the principal measure of the angle ie the angle in `]-pi,pi]`).