Roses specified by the sinusoid ${\displaystyle r=\cos(k\theta )}$ for various rational numbered values of the angular frequency k=n/d. Roses specified by ${\displaystyle r=\sin(k\theta )}$ are rotations of these roses by one-quarter period of the sinusoid in a counter-clockwise direction about the pole (origin). For proper mathematical analysis, ${\displaystyle k}$ must be expressed in irreducible form.