A curve is something that is smooth, continuous and bends.
Now, we’ve explored a ton of curves so far: trigonometric functions, polynomial functions, exponential and logarithmic function, rational functions, conic sections, etc., but wouldn’t it be cool if we could now look at all of these curves from a new perspective and see how each variable is the same, different and changes over time?
Parametric Equations take a common variable, called a parameter, to relate the set of points on a plane curve.
In other words, we are going to define x and y in terms of a third variable, t.
Why? you may ask?
Parametric Equations of a Plane Curve
Well, there are so many things that change over time and are thus connected. For example, your height is a function of your age (time). How far and how long a soccer ball travels when kicked is also a function of time. And, the sun’s position in the sky throughout the course of the day will determine if you need sunglasses.
These are Parametric Functions and as Brightstorm nicely states, a Parametric Equations helps us to describe motion along a curve.
Together we are going to look at five major aspects of Parametric Equations:
- How to represent Parametric Equations.
- Use a table of values to sketch a Parametric Curve and indicated direction of motion.
- Eliminate the Parameter from a pair of equations to get a rectangular equation relating x and y.
- Write a pair of Parametric Equations given a rectangular equation.
- Determine the path of moving object. (i.e., Applications of Parametric Equations)
This video will provide you with the firm foundation for dealing with Parametric Functions in Calculus!
Yes!
Parametric Equations – Video
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