ASKSAGE: Sage Q&A Forum - Individual question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sun, 14 Apr 2013 12:24:14 -0500How to write trgonometric parametrization?http://ask.sagemath.org/question/9986/how-to-write-trgonometric-parametrization/Hello,
Could you please tell me how can I solve a trigonometric parametrization, for example
using a trigonometric identity to show that x= cos(t) y= cos(2t)
parametrizes a portion of a parabola so indicate what portion of the parabola is coverd..
thank youSat, 06 Apr 2013 07:25:17 -0500http://ask.sagemath.org/question/9986/how-to-write-trgonometric-parametrization/Answer by slelievre for <p>Hello,</p>
<p>Could you please tell me how can I solve a trigonometric parametrization, for example </p>
<p>using a trigonometric identity to show that x= cos(t) y= cos(2t)</p>
<p>parametrizes a portion of a parabola so indicate what portion of the parabola is coverd..</p>
<p>thank you</p>
http://ask.sagemath.org/question/9986/how-to-write-trgonometric-parametrization/?answer=14777#post-id-14777Plot 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]`.
Sun, 14 Apr 2013 12:24:14 -0500http://ask.sagemath.org/question/9986/how-to-write-trgonometric-parametrization/?answer=14777#post-id-14777