Thread: Parameterize the motion of an object traveling a circular path.

1. Parameterize the motion of an object traveling a circular path.

Parameterize the motion of an object traveling a circular path clockwise beginning at a point (4,0). The object completes one revolution in 3.14 seconds. It has to be in the form of x=sin( ) and y=cos( ).

2. Re: Need help understanding this please!!!!!!!!!

What have you tried?

Where are you stuck?

3. Re: Need help understanding this please!!!!!!!!!

Your answer can't be in the form x= cos( ), y= sin( ) because will never give (4, 0). Did you mean x= Acos( ), y= Asin( ) for some constant, A?

4. Re: Parameterize the motion of an object traveling a circular path.

Hello, cdiesel89!

Please give us the original wording.

Parameterize the motion of an object traveling a circular path
clockwise beginning at a point (4,0). . Where is the center?

The object completes one revolution in 3.14 seconds.
It has to be in the form: . $x=\sin(\;),\;\;y=\cos(\;)$

The given forms are for a unit circle (radius 1).

There are a brizillion possible circles.
One of them has it center at (3,0).
Its equation is: . $(x-3)^2+ y^2 \:=\:1$
The parametric equations are: . $\begin{Bmatrix}x &=& 3 + \sin\theta \\ y &=& \cos\theta \end{Bmatrix}$

HallsofIvy is correct.

If the center is at the Origin and the radius is to be 4,
. . the forms must have a leading coefficient.

One set of parametric equations is: . $\begin{Bmatrix}x &=& 4\sin\theta \\ y &=& 4\cos\theta \end{Bmatrix}$

If the period is to be $\pi$ seconds, let $\theta = 2t$
. . where $t$ is in seconds.