Has there ever been a time when you didn’t want to follow the same old path? To do something daring and different?
Well, today’s your lucky day! Because graphing points is about to get interesting!
How? you may ask!
Well, think back to when you leaned to plot a point on a graph…. you were told to go left or right along the x-axis and then up or down along the y-axis. That’s all you could do, left-right or up-down.
Things were easy, but not very exciting.
With Polar Coordinates, rather than saying you have to move a certain distance left-right and a certian distance up-down, we’re going to rotate and walk one distance (radius)!
Okay, buy why change things up when we’re used to the easy life of plotting points and moving left-right and up-down?
Representing Polar Coordinates
Well, as you already know, a point in the Rectangular or Cartesian Plane is represented by an ordered pair of numbers called coordinates (x,y). And, these coordinates are directed horizontal and vertical distances along the x and y axes, as Khan Academy points out.
But in the Polar Coordinate System, a point in the plane is determined by its distance (radius) from the origin, now called the Pole, and the angle theta, in radians, between the line from the origin to the point and the x-axis, which is now called the Polar Axis. All we have to do is walk once and then spin.
The reason why we need a new coordinate system is that in some situations the Cartesian coordinate system can be quite difficult to implement (i.e., too difficult to differentiate or integrate). As Oregon State points out, these instances arise when we are dealing with circular, cylindrical, or spherical symmetry.
So, together, we will learn how to:
- Convert Polar to Rectangular Coordinates
- Convert Rectangular to Polar Coordinates
- How to Graph Polar Coordinates
- How to Find Coterminal Coordinate Pairs
- Convert Polar Equation to Rectangular Form
- Convert Rectangular Equations to Polar Curves
Polar Coordinates – Video
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