Question

In algebra we learned about the rectangular (Cartesian) coordinate system. There are other coordinate systems available for us to use, such as polar, cylindrical, spherical, etc. Why would someone want to use a coordinate system other than the rectangular system? Explain and support your arguments using examples.

Answer 1

Polar form is an alternative to rectangular coordinate system. Some uses of polar form are:

1) To find the nth roots of complex numbers
2) To plot circles, spirals, wave curves etc
3) In integrations to find areas (eg: area of circle)

Other coordinate systems like spherical, cylindrical are extremely easier to use in the problems where you have to deal with spherical or cylindrical objects(not only objects,you can show electric fields,potentials).

As a simple example, let us consider a circle of radius a centered at the origin.

In rectangular coordinate system, its equation is x² + y² = a²But its equation in polar coordinates is r=a. The compactness of the equation in polar coordinates can be clearly seen.