Motion of particle

Question

x= 5+2cos(πt) 

y=3+2sin(πt) 

 

1≤t≤2

 

If the pi wasnt there, I know it would be (x-5/2)² +(y-3/2)² =1 ---> (x-5)² + (y-3)² = 4 center(5,3,) and radius=2 

 

For my original equations at the top, since there is a number in front of t , what does this mean ? And how do I convert to a circle equation ? 

Answer 1

x = 5 + 2cos(πt)

y = 3 + 2sin(πt)

 

(x - 5)/2 = cos(πt)

(y - 3)/2 = sin(πt)

 

cos²θ + sin²θ = 1 for ALL θ

 

cos²(πt) + sin²(πt) = 1

 

[(x - 5)/2]² + [(y - 3)/2]² = 1

 

(x - 5)² + (y - 3)² = 2²

 

There is your circle of radius 2 centered at (5,3).

 

The π in front of the t could be some kind of rate in units of (radians)/(units of t), so that when multiplied by t, gives radians, which are dimensionless.  I do not know if you have taken physics, but if you have, think of angular velocity, and then π would be angular velocity in radians/sec, with t in seconds.