Rotating a Point about Origin in a 2D Rectangular Coordinate System

In a 2D rectangular coordinate system, you can rotate a point around the origin, also called making a rotation in Euclidean space. You can get the new coordinates for the rotated point from the relation; x' and y' represent the new coordinates for the point while x and y represent the points orginal coordinates. This rotation is counterclockwise around the origin.

x' = x cos(θ) - y sin(θ)

y' = x sin(θ) + y cos(θ)

If you were looking to rotate the coordinate axes themselves, you can find that here.