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.
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).