A parametric equations grapher is a grapher that draws the range of a function p(t) = [f(t), g(t)] on a given domain in a coordinate system. Such a graph is called the graph of the parametric equations x = f(t) & y = g(t) or the parametric curve represented by the function p(t).
Utilizing the most sophisticated coordinate systems, this parametric equations grapher uses animation to graph parametric curves.
The animated graph shows how parametric curves are constructed not just in the Cartesian but also in the polar coordinate system — actually, it's the only known grapher that is even capable of graphing parametric curves in the polar coordinate system.
You can start animation by pressing ► at the bottom of the graphing area (if it's hidden, press the Animate button first).
It starts the animation of the parametric graphing process of the parametric expression in focus. The graph is drawn progressively from the initial value to the final value of t.
You can then press || to pause the animation or press Done to stop it. This also closes the animation interface. To display it again press the Animate button at the top of the parametric grapher.
You can also change the speed of parametric graphing animation by using the slider provided
In addition, it's also the only parametric curve grapher that enables you to rotate any of the coordinate axes and thus graph parametric curves in non-orthogonal Cartesian coordinate systems.
- pi is replaced by π.
- inf (infinity) is replaced by 2π.
In addition to inputting data — by first pressing the gear button — you can use your mouse to perform some functionality unique to this interactive parametric grapher as outlined below.
- Click on (or near) an axis and move your mouse. That will rotate the axis. The graph(s) are re-drawn in the non-orthogonal (non-perpendicular) Cartesian coordinate system. Click again to release the axis.
- Drag the mouse to move the coordinate system together with the graphs.
- Double-click in the canvas to move the origin to where was clicked.
- Hold down Alt key and click on an axis to change the scale (zoom in one direction); the point which was clicked will be labelled "1" (or "-1") and becomes the new unit for that axis.
Lines
[t, 1] dom=(-5, 5) [1,t] dom=(-5, 5) [t, 2t] dom=(-5, 5)Circles
[4sin(t), 4cos(t)] [3sin(t)+1, 3cos(t)+1]Ellipses
[4cos(t), 3sin(t)] [3cos(t), 4sin(t)] [4sin(t), 3cos(t)] [3sin(t), 4cos(t)]Parabolas
[t, t^2] dom=(-4, 4) [t^2, t] dom=(-4, 4)Hyperbolas
[3sec(t), 4tan(t)] [3tan(t), 4sec(t)]Other parametric graphs
[5sin(t), 4cos(t)] [5sin(t), 4cos(2t)] [5sin(t), 4cos(3t)] [5sin(2t), 4cos(t)] [5sin(2t), 4cos(3t)] [5sin(2t), 4cos(5t)] [5sin(3t), 4cos(5t)] [5sin(3t), 4cos(7t)] [5sin(5t), 4cos(7t)] [5sin(7t), 4cos(9t)]Butterfly curve
[sin(t)(e^cos(t)-2cos(4t)-sin(t/12)^5), cos(t)(e^cos(t)-2cos(4t)-sin( t/12 )^5)] dom=(0, 12π)Lines
[2csc(t), t] [2sec(t), t] [1/(sin(t) - cos(t)), t]Circles
[1, t] [2, t] [6sin(t), t] [8cos(t), t]Spirals
[t, t] [t/5, t] dom=(0, 10π) [√(t), t] dom=(0, 10π) [1/t, t] dom=(0, 10π)Roses
[4sin(3t), t] [4sin(2t), t] [4sin(5t), t] [4sin(4t), t]Ellipses
[1/(1-.8cos(t)), t] [1/(1-.8sin(t)), t] [1/(1+.8cos(t)), t] [1/(1+.8sin(t)), t]Parabolas
[1/(1-sin(t)), t] [1/(1+cos(t)), t] [1/(1+sin(t)), t] [1/(1-cos(t)), t]Hyperbolas
[1/(1+2cos(t)), t] [4/(1+2sin(t)), t] [1/(1-2cos(t)), t] [4/(1-2sin(t)), t]Cardioids
[3+3cos(t), t] [2+2sin(t), t] [3-3cos(t), t] [2-2sin(t), t]Limacons
[2+3cos(t), t] [1+2sin(t), t] [2-3cos(t), t] [1-2sin(t), t]Lemniscates
[√(4sin(2t)), t] [√(4cos(2t)), t]Other parametric graphs
[5sin(t), 4cos(t)] [5sin(t), 4cos(2t)] [5sin(t), 4cos(3t)] [5sin(2t), 4cos(t)] [5sin(2t), 4cos(3t)] [5sin(2t), 4cos(5t)] [5sin(3t), 4cos(5t)] [5sin(3t), 4cos(7t)] [5sin(5t), 4cos(7t)] [5sin(7t), 4cos(9t)]
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