Polar Coordinates: Cartesian Connection (DTube)

In this video I go over further into Polar Coordinates and this time illustrate the connection between polar coordinates and the basic Cartesian coordinate system. As explained in my earlier video, the main difference between polar and Cartesian coordinates is that polar coordinates can be represented in an infinite number of ways due to the circular nature of its definition, as opposed to just one way to represent each point for Cartesian coordinates. Thus in a polar coordinate system, every 360 degrees or 2 pi radians (i.e. a full rotation of a circle), we obtain the same value, thus it comes to no surprise that in representing polar coordinates as Cartesian coordinates, we need to use trigonometry, which also share this property. Using the definition of trigonometry, and combining both the Polar and Cartesian coordinate system, we can write x and y by the following formulas:

x = r cosθ
y = r sinθ

If we were instead trying to solve for r and θ, i.e.. the polar coordinates, if we were given x and y, then we can use the Pythagorean theorem along with the definition of the tangent trigonometric function to get the following formulas:

r² = x² + y²
tanθ = y/x

Thus from these equations we can switch easily from Polar and Cartesian coordinates, and vice-versa. This is a great video to illustrate just how the two coordinate systems are different, yet at the same time inter-connected, so make sure to watch this video because I will be building upon it in some crazy advanced math concepts!!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhugUhXpoEDWEwUQVQw

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/video-notes-polar-coordinates-cartesian-connection