http://www.ck12.org Chapter 10. Polar and Parametric Equations
10.5 Applications of Parametric Equations
Here you will use parametric equations to represent the vertical and horizontal motion of objects over time.
A regular function has the ability to graph the height of an object over time. Parametric equations allow you to
actually graph the complete position of an object over time. For example, parametric equations allow you to make a
graph that represents the position of a point on a Ferris wheel. All the details like height off the ground, direction,
and speed of spin can be modeled using the parametric equations.
What is the position equation and graph of a point on a Ferris wheel that starts at a low point of 6 feet off the ground,
spins counterclockwise to a height of 46 feet off the ground, then goes back down to 6 feet in 60 seconds?
Watch This
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/62062http://www.youtube.com/watch?v=m6c6dlmUT1c Academy: Parametric Equations 1
Guidance
There are two types of parametric equations that are typical in real life situations. The first is circular motion as was
described in the concept problem. The second is projectile motion.
Parametric equations that describe circular motion will havexandyas periodic functions of sine and cosine. Eitherx
will be a sine function andywill be a cosine function or the other way around. The best way to come up with
parametric equations is to first draw a picture of the circle you are trying to represent.