Question

X= 2 cos³t y = 2 sin ³ t
find the cartesian equation

Answer 1

`y^2 = x^3 / 2^(3/2)` or
`y = x^(3/2) / 2^(3/4)`

Explanation:

We can use the identity
`cos^3(t) = cos(t)*cos^2(t) and sin^3(t) = sin(t)*sin^2(t)` to rewrite the given parametric equations in terms of x and y:

`x = 2cos(t)*cos^2(t) = 2x^2 - 2y^2`

`y = 2sin(t)*sin^2(t) = 2xy^2`

Solving for y in terms of x, we get:

`y = x^(3/2) / 2x^(3/4)`

Therefore, the cartesian equation of the curve is:

`y = x^(3/2) / 2^(3/4)`

or, equivalently:

`y^2 = x^3 / 2^(3/2)`