Parametric equations and polar coordinates
Plot a curve from parametric equations point by point, eliminate the parameter, model a motion and convert polar coordinates to Cartesian.
- سوريا: الصف ١١
- بريطانيا: السنة ١٣
لم يُترجَم هذا المختبر إلى هذه اللغة بعد.
الدليل
Sometimes x and y both depend on a helper variable t (the parameter): x = ٢t, y = t٢. Each t gives one point and many values of t draw the curve. To eliminate the parameter, make t the subject of one equation and substitute it into the other: t = x٢ and y = (x٢)٢.
The parameter is often time. The path of a ball can be modelled with x = vt and y = ut − ١٢gt٢; the ball lands when y = ٠.
In polar coordinates a point is given by its distance r from the origin and its angle θ from the positive x-axis. Converting: x = rcosθ, y = rsinθ. A polar curve such as r = ٢ + ٢cosθ is plotted point by point from a table of (θ, r).