The following two sets of parametric functions both represent the same ellipse. Explain the difference between the graphs.
x = 3 cos t and y = 8 sin t
x = 3 cos 4t and y = 8 sin 4t
1 answer
The two sets of parametric functions represent the same ellipse, but the difference lies in the speed at which the ellipse is traced out. The first set of functions, x = 3 cos t and y = 8 sin t, traces out the ellipse at a slower rate as t varies, resulting in a smoother, more elongated ellipse. On the other hand, the second set of functions, x = 3 cos 4t and y = 8 sin 4t, traces out the ellipse at a faster rate as t varies, resulting in a more compressed and jagged ellipse. In other words, the second set of functions produces a more quickly oscillating ellipse compared to the first set.