Which of the following correctly gives the parametric (x,y) representation of a polar curve r = f(θ)?

x = cos(f(θ)), y = sin(f(θ)) — an incorrect composition that treats r as an angle rather than a radial distance

x = f(θ) sin θ, y = f(θ) cos θ — a plausible swap of trig factors but incorrect because x should multiply cos θ and y should multiply sin θ

x = f(θ) cos θ, y = −f(θ) sin θ — superficially similar but incorrect sign for the y coordinate

x = f(θ) cos θ, y = f(θ) sin θ