# polar coordinates

## The Polar Coordinate System

In Polar Coordinate System, the references are a fixed point and a fixed line. The fixed point is called the **pole** and the fixed line is called the **polar axis**. The location of a point is expressed according to its distance from the pole and its angle from the polar axis. The distance is denoted by r and the angle by θ.

## Length of Arc in Polar Plane | Applications of Integration

The length of arc on polar plane is given by the formula:

$\displaystyle s = \int_{\theta_1}^{\theta_2} \sqrt{r^2 + \left( \dfrac{dr}{d\theta} \right)^2} ~ d\theta$

The formula above is derived in two ways. See it here: http://www.mathalino.com/reviewer/integral-calculus/length-arc-polar-pla...

## 05 Area Enclosed by Four-Leaved Rose r = a cos 2θ

Find the area enclosed by four-leaved rose r = a cos 2θ.

## Plane Areas in Polar Coordinates | Applications of Integration

The fundamental equation for finding the area enclosed by a curve whose equation is in polar coordinates is...

$\displaystyle A = \frac{1}{2}{\int_{\theta_1}^{\theta_2}} r^2 \, d\theta$