Introduction

We introduce another type of coordinate system here. It will be useful while handling some curves since it can simplify the equation. In the future, choosing appropriate coordinate system is one of the key point for solving problems in calculus.

Representation of Positions

In Polar Coordinates, we use two values to represent the position of points: its distance from the pole ${\displaystyle r}$ and the angle made by the ray emanating from the pole passing through the point ${\displaystyle \theta }$.

The notation is ${\displaystyle (r,\theta )}$.

But the representation is not the only one. Since the direction of the pole axis can be different and can rotates ${\displaystyle 2\pi n}$ degrees.

Relation to Cartesian Coordinate

From ${\displaystyle (x,y)}$ to ${\displaystyle (r,\theta )}$, we have relationship listed below:

• ${\displaystyle x=r\cos \theta }$
• ${\displaystyle y=r\sin \theta }$
• ${\displaystyle x^2+y^2=r^2}$
• ${\displaystyle \frac{y}{x}=\tan \theta }$
  We can easily transfer positions in cartesian coordinates into polar coordinates.