Revision history [back]
 | 1 | initial version |
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].
| | 2 | No.2 Revision |
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].
