14.2. Parametric Equations
A parametric equation of a curve expresses the points on the curve as an explicit function of "parameters" or indepedent variables usually denoted by t. Examples of parametric equation are: x = t^2 - t, y = 3t + 1, x = 3cost, y = 2sint, cos^2(t) + sin^2(t) = 1, and x = cos(3t). Type the equation as given with one equation per line.
Example 1
Sketch the graphs of the following parametric equations.
Example 1
Sketch the graphs of the following parametric equations.
x = t2 – t y = 3t + 1
Calculator solution
Enter each of the following.
1) x = t^2 - t
2) y = 3t + 1
Enter each of the following.
1) x = t^2 - t
2) y = 3t + 1
Example 2
Sketch the graphs of the following parametric equations.
Sketch the graphs of the following parametric equations.
x = cos t y = sin t
Calculator solution
Enter each of the following.
1) x = cos t
2) y = sin t
Enter each of the following.
1) x = cos t
2) y = sin t
Example 3
Sketch the graphs of the following parametric equations.
Sketch the graphs of the following parametric equations.
x = 3 cos t
y = 2 sin t
Calculator solution
Enter each of the following:
1) x = 3 cos t
2) y = 2sin t
Enter each of the following:
1) x = 3 cos t
2) y = 2sin t
Example 4
Sketch the graphs of the following parametric equations.
Sketch the graphs of the following parametric equations.
x = cos 4t
y = sin 5t
Calculator solution
Enter each of the following.
1) x = cos 4t
2) y = sin 5t
Enter each of the following.
1) x = cos 4t
2) y = sin 5t
Example 5
Sketch the graphs of the following parametric equations.
Sketch the graphs of the following parametric equations.
x = cos 10t y = sin 11t
Calculator solution
Enter each of the following.
1) x = cos 10t
2) y = sin 11t
Enter each of the following.
1) x = cos 10t
2) y = sin 11t