Plot the graph of the hypocycloid

For appropriate values oft in each of the following cases:
a. a = 4, b = 1
b. a = 3, b = 1
c. a = 5, = 2
d. a = 7, b = 4
Experiment with other positive integer values of a and b and then make conjectures about the length of the t-interval required for the curve to return to its starting point and about the number of cusps. What can you say if a/b is irrational?

x # (a-b) cost + b cos 4- t. y (a b) sin - b sin a-b