Question

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

Answer 1

One way of doing this is to list some convenient values of \(t\), then determine they corresponding \(x\) and \(y\) values.

For example, it's easy to find the sine and cosine of \(\pi\). So let \(t=\pi\). For this \(t\), you get
\[\begin{cases}x=3\sin^3\pi=3(0)^3=0\\
y=3\cos^3\pi=3(1)^3=3\end{cases}\]
So when \(t=\pi\), you have the point \((0,3)\).

You'd keep going in this manner. Keep track of the path of \((x,y)\) as \(t\) varies. From what I remember, you have to show the path of the curve when graphing parametric curves.

Answer 2

@lbouskila, does that make sense?

Answer 3

so what do intervals do i use?

Answer 4

like 0, pi, then what?

Answer 5

What other \(t\)-values make it easy? Go for the convenient ones, like \(\dfrac{\pi}{2},\dfrac{\pi}{4},...\).

Answer 6

so im doing it wrong if im getting number values?

Answer 7

so what im doing is finding values for t, plugging them in and solving for the x and y values that ultimately go into my graph?

Answer 8

@SithsAndGiggles

Answer 9

and do i put in negatives?

Answer 10

You can use negatives since there is no restriction on \(t\), but you'll find that many points are repeated. Here's a small table: