Question

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

Answer 1

Hello,

This is an astroïde.

(x/3)^(2/3)+(y/3)^(2/3)=1

Answer 2

Answer with explanation:

We are given a parametric equation as:

`x=3 \sin^3 t`

and
`y=3 \cos^3 t`

Hence, we can represent our equation as:

`\sin^3 t=(x)/(3)\\\\\\\sin t=((x)/(3))^{(1)/(3)}\\\\\\Hence,\\\\\sin^2 t=((x)/(3))^{(2)/(3)}\\\\and\ similarly\\\\\cos^3 t=(y)/(3)\\\\\cos t=((y)/(3))^{(1)/(3)}\\\\Hence,\\\\\cos^2 t=((y)/(3))^{(2)/(3)}`

As we know that:

`\cos^2 t+\sin^2 t=1`

Hence, on putting the value in the formula we get the equation in rectangular coordinates as:

`((x)/(3))^{(2)/(3)}+((y)/(3))^{(2)/(3)}=1`

Hence, this is a equation of a ASTROID.