In the following figure, as we mentioned before the blue ones are showing the equation. It is the general case of the graphs of the equation according to the Position of the tracing point. That is to say, if a point is inside of the circle, then it will be red one and if a point is outside of the circle, then it will be green one. OA defines the radius of the circle, C is the point of segment between the point on the circle and the center of the circle, and D is an outside point on the extension of the segment connection center and the point on the circle. Let's use another graphic program, Theorist.
Theorist is one of the good graphic programs which can show the parametric function very well.
A cycloid is the locus of points of a point on a circle rolling along a line without slipping. Let's see the types of cycloid for different radius values. For example, when the radius of circle is 2 then the graph is the following. Let's discuss the role of t. There is another thing that we need to talk about.