Parametric Equations

Question

$x=3\sin^3t$

$y=3\cos^3t$

How would I even begin to work out this one? I'm supposed to graph it, but I have no clue what how to even start it.

Answer 1

Using the identity $\sin^2 t + \cos^2 t = 1$, we can conclude that $(3 \sin^{3} t)^{2/3} + (3 \sin^{3} t )^{2/3} = 3^{2/3}$, that is, $x^{2/3} + y^{2/3} = 3^{2/3}$. From that point, you can differentiate implicitly to find the critical points, inflection points, regions of increase/decrease, etc. (as you normally would when attempting to graph a function $y(x)$).

Answer 2

There is a point for every value of angle t. For each, substitute it into the expression for x, then into the expression for y. Taken together, the two constitute the coördinates of a point on your desired graph. Do you know how to plot points on a Cartesian plane?