Assignment 10:
Parametric Curves
A parametric curve in the plane is a pair of
functions
where the two continuous functions define
ordered pairs (x,y). The two equations are usually called the parametric
equations of a curve. The extent of the curve will depend on the range of t.
In many applications, we think of x and y as
"varying with time t " or the angle of rotation that some line makes from
an initial location.
For this assignment, I will be using Graphing Calculator 3.2.
Let's Start Our Investigation by Looking at the Following Parametric Equations:
x = cos(t)
y = sin(t)
where t ranges from 0 to 2pi
What do you think the graph will look like?
Click here to see if you are right!
Now Let's Change the Equation a Little!
For various a and b, investigate:
x = cos(at)
y = sin(bt)
where t ranges from 0 to 2pi
What do you think the graph will look like when a = b?
Click here to see if you are right!
What do you think the graph will look like when a > b?
Click here to see if you were right!
What do you think the graph will look like when a<b?
Click here to see if you were right!
Do you see a pattern forming from our observations?
Click here to see if you have made the same observation as me!
I have another idea ... maybe my observation only works when 'a' or 'b' is 1 and 'a' is an odd number!
Click here to see if I am on the right track!