Polar coordinates are simply a way of defining the position of a point in 2 dimensions. The distance from the origin (r) and the angle made with the x axis (measure in an anti-clockwise direction) define the position of the point. The point in the above diagram is a distance 3 from the origin and the angle made with the x axis is 30°.
This tutorial from analyzemath.com will help you understand how to plot polar coordinates; it will also help you understand why there is more than one way to specify a particular point.
For example, try plotting (3, 60), (3,-300) Note the other suggestions in the tutorial.
Explore polar curves using David Little’s applet.
It is possible to see how polar curves are traced out by using a slider in the domain on the Desmos graphing calculator. Try this example showing r=acoskθ.
Further examples: r=acos2θ, r=a(1-cosθ) r=ae-kθ
See also The Polar Gallery from mathsdemos.org. If you scroll down the page you will see that you can download a set of 14 Excel files which will allow you to experiment with several families of polar curves.