Cardioid via polar curve equation
The f(x) function equation of a sinusoid is entered by default in the rectangular (a.k.a. Cartesian) coordinate input box. To its right, the corresponding r(θ) equation for a polar curve is displayed.
This construction is intended to help those new to polar coordinates see the connection between the y values on the rectangular graph (vertical line segments on 0≤x≤2π) and the r values on the polar graph (line segments radiating outward from origin/pole on 0≤θ≤2π).
The default polar curve is a "cardioid," but changing the equation will create different types of polar curves.
This construction allows zooming/panning, and the cyan + may be dragged to move the polar graph relative to the rectangular graph.
The "c" slider will be visible as long as a "c" or "C" is present in the formula text (outside of the spelling of operators cos, csc, cot, and ceil).