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

1 Answer
A. S. Adikesavan
Jan 8, 2017

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]}

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