Find the polar coordinates of the points with cartesian coordinates (−x, y).

The polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction. Polar coordinates are used while representing various spherical objects in engineering and science. It is very easy to convert cartesian coordinates to polar coordinates.

Answer: The cartesian coordinates (-x, y) can be represented in polar coordinates by (r, Ø), where r = √(x² + y²) and Ø = π - tan^-1(y/x).

Let's understand the solution.

Explanation: 

If we consider the point (x, y); if we want to represent it in polar coordinates, then we have polar coordinates as (r, Ø), where r = √(x² + y²), and Ø = tan^-1(y/x).4

This is for the points in the first quadrant.

But, if the points are in the second quadrant (like (-x, y), where x, y > 0), then the magnitude remains the same, but the phase changes to π - tan^-1(y/x).

Hence, the cartesian coordinates (-x, y) can be represented in polar coordinates by (r, Ø), where r = √(x² + y²) and Ø = π - tan^-1(y/x).