please explain how to find the parametric eq.

**pnfuller** · August 30th 2012, 06:13 PM

find parametric equations for the path of particle that moves along x²+(y-1)²=4 in a manner described.....

A.) once around clockwise, starting at (2,1)
B.) three times around counterclockwise, starting at (2,1)
C.) halfway around counterclockwise, starting at (3,0)

please help!!!!! and explain in detail please, i dont understand this AT ALL!!!

**Prove It** · August 30th 2012, 07:38 PM

Originally Posted by pnfuller

find parametric equations for the path of particle that moves along x²+(y-1)²=4 in a manner described.....

A.) once around clockwise, starting at (2,1)
B.) three times around counterclockwise, starting at (2,1)
C.) halfway around counterclockwise, starting at (3,0)

please help!!!!! and explain in detail please, i dont understand this AT ALL!!!

Do not double post.

**MaxJasper** · August 30th 2012, 08:42 PM

Originally Posted by pnfuller

find parametric equations for the path of particle that moves along x²+(y-1)²=4 in a manner described.....

A.) once around clockwise, starting at (2,1)
B.) three times around counterclockwise, starting at (2,1)
C.) halfway around counterclockwise, starting at (3,0)

please help!!!!! and explain in detail please, i dont understand this AT ALL!!!

Equation of this circle with radius=2 and center=(1,0) in complex plane is:

$z(\theta \)\text{=}1+2 e^{i \theta }$

Let t1, t2, t3 be 3 parameters representing stages 1,2,3 of rotation. Then the path is:

$path=\left[e^{-2 \pi i t_1} e^{\left(6 \pi -\frac{\pi }{4}\right) i t_2} e^{\pi i t_3} z\left(\frac{\pi }{4}\right)\right]$

Simplifying we have:

$path= \sqrt{2} \sin \left(2 \pi t_1-\pi t_3-\frac{23 \pi t_2}{4}\right)+\sqrt{2} \cos \left(2 \pi t_1-\pi t_3-\frac{23 \pi t_2}{4}\right)+\cos \left(2 \pi t_1-\pi t_3-\frac{23 \pi t_2}{4}\right)+i \left(-\sqrt{2} \sin \left(2 \pi t_1-\pi t_3-\frac{23 \pi t_2}{4}\right)-\sin \left(2 \pi t_1-\pi t_3-\frac{23 \pi t_2}{4}\right)+\sqrt{2} \cos \left(2 \pi t_1-\pi t_3-\frac{23 \pi t_2}{4}\right)\right)$

Notice that horizontal component of particle's location is real part of path and its verttical component as imaginary part of the path.

$x(t)=\sqrt{2} \sin \left(2 \pi t_1-\pi t_3-\frac{23 \pi t_2}{4}\right)+\sqrt{2} \cos \left(2 \pi t_1-\pi t_3-\frac{23 \pi t_2}{4}\right)+\cos \left(2 \pi t_1-\pi t_3-\frac{23 \pi t_2}{4}\right)$

$y(t)=-\sqrt{2} \sin \left(2 \pi t_1-\pi t_3-\frac{23 \pi t_2}{4}\right)-\sin \left(2 \pi t_1-\pi t_3-\frac{23 \pi t_2}{4}\right)+\sqrt{2} \cos \left(2 \pi t_1-\pi t_3-\frac{23 \pi t_2}{4}\right)$

Thread: please explain how to find the parametric eq.

LinkBack

Thread Tools

Display

please explain how to find the parametric eq.

Re: please explain how to find the parametric eq.

Re: please explain how to find the parametric eq.

Similar Math Help Forum Discussions

Can somebody explain why you take the derivative of a curve to find its length?

Find X? show and explain steps to find x

Can Someone Explain This Answer? Find an angle given other angles

Can some one explain hwo to find probability?

Anyone can explain how to find eigenvectors?

Search Tags