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Every torus knot can be represented as a Fourier-(1,1,2) knot which is thesimplest possible Fourier representation for such a knot. This answers aquestion of Kauffman and confirms the conjecture made by Boocher, Daigle, Hosteand Zheng.  In particular, the torus knot T(p,q) can be parameterized as x(t)=cos(pt),y(t)=cos(qt+pi/(2p)), and z(t)=cos(pt+pi/2)\cos((q-p)t+pi/(2p)-pi/(4q)).

TORUS KNOTS ARE FOURIER-(1,1,2) KNOTS