Question

How do you write an equation for a rose with 3 petals?

Answer 1

In the parametric form, `r=a cos 3(theta-alpha)`, where the size a and rotation angle `alpha` are parameters, at your choice. The inserted graphs are for a = 1, and `alpha=0 and -pi/2`.

Explanation:

The general equation to an n-petal rose is

`r = a cos n(theta - alpha )`, where a and `alpha` are at your choice and n = 2, 3, 4, ....

The inserted graphs are for

`r = cos 3theta`, for a = 1 and `alpha = 0` and

`r = sin 3theta`, for a = 1 and `alpha = -pi/2.`

The equations for graphing are in cartesian form.

graph{(x^2+y^2)^2-3x(x^2+y^2)+4x^3=0 [-2.5, 2.5, -1.25, 1.25]}

graph{(x^2+y^2)^2+y(x^2+y^2)-4x^2y=0 [-2.5, 2.5, -1.25, 1.25]}