From Polar to Cartesian Coordinates
We can represent the position of a point in the plane not only by its Cartesian coordinates , but also by its polar coordinates .
Interact with the app below to explore the relationship between the two coordinate systems.
Some Considerations
It is customary to assign to the polar axis (corresponding to ) the same direction of the -axis of an orthogonal Cartesian system, and to make the pole coincide with the origin, in order to simplify the conversion between the two systems.
With this convention, the -axis of the Cartesian system corresponds to in the polar system.
Polar functions will not have the Cartesian form , but instead the polar form .
Practice Zone
Determine the inverse formulas of the conversion formulas described in the app. The inverse formulas allow you to obtain the polar coordinates of a point whose Cartesian coordinates are known. Use these formulas to calculate the polar coordinates of the point whose Cartesian coordinates are .
The coordinates of the following points are given in polar form. and . Plot these points in a polar coordinate system. Do you notice anything?