Sketching parametric curves
In a nutshell
The majority of parametric curves will not result in curves you can easily recognise and sketch. The best way to plot parametric curves is to substitute values of the parameter into each of the equations.
Sketching a parametric curve
Tabulate the values of t,x and y using the parametric equations, then plot points and sketch the curve.
Example 1
Draw the curve given by the parametric equations:
x=2sin(t)+3,y=5cos(t),0≤t≤2π
Choose values for t, spanning the domain given in the question. For each value of t, substitute to find the corresponding x and y values, which will be the coordinates of the points on the curve.
t | | | | 43π | | 45π | 23π | | |
x=2sin(t)+3 | | | | | | | | | |
y=5cos(t) | | | | | | | | | |
Plot the points and draw a curve through the points. This graph is an ellipse.
Example 2
Draw the curve given by the parametric equations:
x=2t−3,y=t2−1,−2≤t≤2
Choose values for t, spanning the domain given in the question. For each value of t, substitute to find the corresponding x and y values, which will be the coordinates of the points on the curve.
Plot the points and draw a curve through the points.