Bound the y values to anything you like, but to keep consistent with cosine and sine you may want to bound them between -1 and 1.
Bound the x values between -180 and 180 (if you're working in degrees) or however quickly you think people will get the point. Every 90 degrees draw a x^3 style line and draw dotted lines to symbolise the asymptotes.
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Yes, that is a shifted tanX graph, just as you would shift any graft.
-2
12
-2
That line is [ y = 2 cos(2x) ].