Differentiation of Polar Equations**
The reference point is called the pole, and the ray from the pole in the reference direction is the polar axis.
The radial coordinate is often denoted by r, and the angular coordinate by θ.
Polar coordinates are most appropriate in any context where the phenomenon being considered is inherently tied to direction and length from a center point.
The mathematical function that describes a spiral can be expressed using rectangular (or Cartesian) coordinates.
However, if we change our coordinate system to something that works a bit better with circular patterns, the function becomes much simpler to describe.
The polar coordinate system is well suited for describing curves of this type.
Many physical systems—such as those concerned with bodies moving around a central point or with phenomena originating from a central point—are simpler and more intuitive to model using polar coordinates.