Question

Graph each pair of parametric equations.
x = 3 sin^3t
y = 3 cos^3t

Answer 1

Well since the equations are given to you like that, in order to graph it you want to get rid of t, then you can make a table of values for x & y.

Answer 2

so \[x=3\sin^3t \rightarrow \frac{ x }{ 3 } = \sin^3t\] & \[y=3\cos^3t \rightarrow \frac{ y }{ 3 } = \cos^3t\]

You want to have cos^2t + sin^2t since that is the equation for a circle. so to get that you would have \[(\frac{ x }{ 3 })^\frac{ 2 }{ 3 } + (\frac{ y }{ 3 })^\frac{ 2 }{ 3 } = 1\] . Now plug in points and you can graph the equation.