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How to write trgonometric parametrization?

asked 2013-04-06 07:25:17 -0600

Neda gravatar image


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 you

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answered 2013-04-14 12:24:14 -0600

updated 2013-04-14 12:24:50 -0600

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].

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Asked: 2013-04-06 07:25:17 -0600

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Last updated: Apr 14 '13