Cardioid Circle Graph. Polar equation of the common cardioid is ra 1cos theta r a1 cosθ. If possible animate this to make understanding easier.
The cardioid is symmetrical about the positive axis and the point of indentation is at the pole. Here is a picture with the entire cardioid and most of the circle shown. Sketch the graph of the cardioid r 1 cos t and the circle r 3cos t Shade the region that is outside of the cardioid and inside of the circle.
If possible animate this to make understanding easier.
This graph is obtained by tracing out the path of a circle rolling over another fixed circle. Set r1 1 Set r2 1 cos Use a 02 x -44 x -22 viewing window The area inside the circle and outside the cardioid lies in the first and fourth quadrants. The bulk of the graph is to the right of the y-axis when a and b are positive and to the left of the y-axis when a and b are negative. The path that point traces is a cardioid.
