Consider the path where a, b, and ω are positive constants and a > b. T (a)...

Consider the path

where a, b, and ω are positive constants and a > b.

T (a) Use a computer to plot this path when

i. a = 3, b = 1, and ω = 15.

ii. a = 5, b = 1, and ω = 15.

iii. a = 5, b = 1, and ω = 25.

Comment on how the values of a, b, and ω affect the shapes of the image curves.

(b) Show that the image curve lies on the torus

(A torus is the surface of a doughnut.)