On the curve generated by plotting one sine against another

A circle? A line? Actually, it depends. It depends upon parameters like the frequency or the phase; when these change, really interesting things happen. What I mean by “against another” is that the first sine function will be the x-coordinate while the other, the y-coordinate; then, if you studied engineering you might say “y vs. x” but if you studied biology you might be used to say “x vs. y” (personal observation). We end up then with a curve, say \gamma(t) = (x(t), y(t)), where

x(t) = A_1\sin(\omega_1 t + \phi_1)

and

y(t) = A_2\sin(\omega_2 t + \phi_2).

Continue reading On the curve generated by plotting one sine against another

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