Describe the motion of the particle

Question

x= 2sint

y=4+ cost 

 

0≤t≤3pi/2 

 

I dont understand the solution. My solution booklet says that the particle starts at ( 0,5) and moves clockwise and ends at ( -2,4) . I only got to solving the parametric equations to get (x/2)² + (y-4)² =1 . Why does it start at (0,5) and ends at ( -2,4) ?

Answer 1

x(0) = 2sin(0) = 0

y(0) = 4 + cos(0) = 4 + 1 = 5

 

You can see that at t = 0, it starts at (0,5).

 

x(3π/2) = 2sin(3π/2) = 2(-1) = -2
y(3π/2) = 4 + cos(3π/2) = 4 + 0 = 4

 

You can see that at t = 3π/2, it is at (-2,4).

 

Note that (0,5) and (-2,4) satisfy your equation

 

(x/2)² + (y - 4)² = 1.