Determine the parametric equations of the path of a particle that travels the ci

Question

Determine the parametric equations of the path of a particle that travels the circle:

Incorrect. Tries 1/8 Previous Tries Determine the parametric equations of the path of a particle that travels the circle: y( t ) = traveling clockwise x( t ) = Tries 0/8 if the particle makes one half of a circle starting at the point y( t ) = traveling clockwise x( t ) = Incorrect. Tries 1/8 Previous Tries if the particle makes one full circle starting at the point y( t ) = traveling counterclockwise x( t ) = if the particle makes one full circle starting at the point on a time interval of

Explanation / Answer

The parametric equation of the circle is x = 1+3 cost and y = 2+3 sin t

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Since the particle starts at the point (4,2) we have for t=0 x=4 and y =2

Substitute in the parametric equations. We see that the equation gets satisfied.

So x(t) = 1+3 cost and y = 2+3 sint , t varies from 0 to 2pi.

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If particle starts at (1,5) we have initial position as x=1 and y =5 and travels clockwise.

x = 1+3 cos(pi/2-t) Then initial position will be 1.

y = 2+3 sin (pi/2-t) Then initial position for y will be 5

Thus we have x = 1+3 cos u and y = 2+ 3 sin u where u = -(pi/2 -t) or u = t-pi/2 and u varies from -pi/2 to 3pi/2.

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If the particle covers half circle starting from (4,2)

then equation is x = 1+3 cost , y = 2+3sin(-t) as clockwise or

x = 1+3 cost , y = 2-3sin(t)

and t varies from 0 to -pi. This gives the half circle.clockwise.

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