Roses specified by the sinusoid r = cos(kθ) for various rational numbered values of the angular frequency k = n/d. Roses specified by r = sin(kθ) 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, k must be expressed in irreducible form. In mathematics, a rose or rhodonea curve is a sinusoid