How to write trgonometric parametrization?

Neda
65 ●5 ●10 ●20

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 you

1 Answer

Sort by » oldest newest most voted

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].

Please start posting anonymously - your entry will be published after you log in or create a new account.

1 follower

Asked: 2013-04-06 14:25:17 +0100

Seen: 337 times

Last updated: Apr 14 '13