<p>I'm studying the Barron's guide for Math II, and it doesn't really explain parametrics well. Is it necessary to understand for the test, or should I skip it? </p>
<p>If anyone knows what they are and can point me in the direction of an online resource/can explain it to me, I would greatly appreciate it.</p>
<p>Thanks!</p>
<p>A parametric function is a function that is split up into two components. It has a constant incrementor “t” which starts at 0 and goes up from there.
For example:
x = t
y = 2t</p>
<p>The point at t= 0 would be (0,0) at t=1 it would (t,2t) or (1,2) since t= 1, at t=2 it would be (t,2t) or (2,4).
I like to think of T as time, you can’t have negative time and it increases naturally to infinity and as t changes so do the coordinates it represents.</p>
<p>Eliminating the Parameter: (Find an XY function that represents the parametric function)
Method 1: Substitution.
Example:
y=t^3
x=t^2
What I like to do is solve for X in terms of t and then “substitute” x into the y equation.
sqrt(x)=t
therefore,
y=(sqrt(x))^3
= x^(3/2)
y = x^3/2
Method 2: Using Trig Identities
x= (sin t)^2
y=(cos t)^2
Now remember cos^2(any number)+sin^2(any number)= 1 where the (any number) is the same in both of cos^2 and sin^2 is always equal to 1.
So just substitute, t is the same in both, therefore x+y = 1
or y=-x+1</p>