# Revision history [back]

Plot the curve to gain intuition. Obviously 2*pi is a period, so it is enough to plot the curve for t varying in [0,2*pi].

sage: t = var('t')
sage: parametric_plot((cos(t),cos(2r*t)),(t,0r,2r*float(pi)))


To get a formula for y as a function of x, you can use simplify_trig.

sage: cos(2*t).simplify_trig()
2*cos(t)^2 - 1


Confirm the portion of the parabola indicated by the plot by observing that x = cos(t) means x varies in [-1,1].

Plot the curve to gain intuition. Obviously 2*pi is a period, so it is enough to plot the curve for t t varying in [0,2*pi].

sage: t = var('t')
sage: parametric_plot((cos(t),cos(2r*t)),(t,0r,2r*float(pi)))


To get a formula for y as a function of x, you can use simplify_trig.

sage: cos(2*t).simplify_trig()
2*cos(t)^2 - 1


Confirm the portion of the parabola indicated by the plot by observing that x = cos(t) means x varies in [-1,1].