Parametric and Polar Coordinates
Parametric and Polar Coordinates are an important section of the AP Calculus BC exam. In this module, we cover concepts involving differentiation and integration in these coordinate systems.
Introduction to Parametric Coordinates
In this video, I introduce parametric coordinates and how they are used.
Parametric Graphing Resource
In this video, I use desmos.com as an easy way to graph parametric curves.
In this video, I cover how to eliminate t so that you can go from parametric to Cartesian coordinates (or vice versa by introducing t).
Here I introduce how to take derivatives in parametric coordinates using the chain rule.
In this video, I cover how to write the equations for tangent lines in parametric coordinates (there could be multiple!).
Area in Parametric Coordinates
Here I cover how to find the area in parametric coordinates using integration.
Arc length is an important concept to know for the AP Calc BC exam. It is covered in this video.
Volume and Surface Area in Parametric Coordinates
I cover how to find the volume of solids of revolution in parametric coordinates. In addition, I go over how to find the surface area of the...
Introduction to Polar Coordinates
Now, we move on to polar coordinates. This is the introduction, covering what polar coordinates are and how to go from Cartesian to polar or...
Graphing Polar Curves
Here I use desmos.com to show the vast number of possibilities in polar coordinates.
Now we introduce the calculus aspect of polar coordinates, starting with derivatives.
Area in Polar Coordinates
In this video, I cover how to find the area enclosed by a polar curve (a key point that it is enclosed NOT under the curve).
Area Between Polar Curves
In this video, I cover how to find the area between two polar curves with an example.
Arc Length and Surface Area in Polar Coordinates
In this video, I'll cover how to find the length of a polar curve and the surface area of a solid of revolution in polar coordinates. Toward...