Question

In what situations would you change to cylindrical or spherical coordinates?

Short answer

When our solid is more easily described using some other system we change to different coordinates.

Step-by-step solution

Define the coordinates matrix

A change of coordinates matrix, also called a transition matrix, specifies the transformation from one vector basis to another under a change of basis.

Explain the need to change the coordinates.

It is usually a good idea to change to cylindrical or spherical coordinates if our solid is easier described using them than the rectangular coordinates.

Cylindrical coordinates are usually used when our solid is a cylinder or a part of one. Spherical coordinates are usually used when our solid is a sphere, cone, spherical shell, or something similar that is part of a sphere.

So, we change to different coordinates when our solid is more easily described using some other system.