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( ).
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( ).
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: .$\displaystyle x=\sin(\;),\;\;y=\cos(\;)$
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: .$\displaystyle (x-3)^2+ y^2 \:=\:1$
The parametric equations are: .$\displaystyle \begin{Bmatrix}x &=& 3 + \sin\theta \\ y &=& \cos\theta \end{Bmatrix}$
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: .$\displaystyle \begin{Bmatrix}x &=& 4\sin\theta \\ y &=& 4\cos\theta \end{Bmatrix}$
If the period is to be $\displaystyle \pi$ seconds, let $\displaystyle \theta = 2t$
. . where $\displaystyle t$ is in seconds.