Polar Equations vs Rectangular Equations - Calculus 2

When working in the polar coordinate system rather than in the rectangular coordinate system, you will no longer be using rectangular equations in terms of x and y. Instead, you will be using brand new types of equations known as polar equations.

Similar to how rectangular equations in the form of y=f(x) create pairs of x-coordinates and y-coordinates, polar equations create pairs of polar coordinates, including a radius r and an angle θ. As such, polar equations are typically in the form of r=f(θ), where the value of the radius (r) is represented as a function of theta (θ).

Just like rectangular equations, polar equations can be graphed in a coordinate system. While the actual method of graphing polar equations will be the focus of the next lesson, it is still important to realize that there are some graphs, such as graphs of lines and circles, that can be represented by equations of both rectangular form and polar form. In fact, we can convert between the rectangular and polar form of an equation for a particular graph by using the conversion formulas for polar coordinates and rectangular coordinates. This concept of converting from polar equations to rectangular equations and vice versa will be the main focus this time around.

We discuss all of this and more in this new lesson of Calculus 2. Let's get to it!

In this lesson, you will learn:

• How polar equations and rectangular equations are related
• How to convert polar equations to rectangular form
• How to convert rectangular equations to polar form

I hope you find this video to be helpful!

-Josh