Question

Describe the motion of a particle with position (x, y) as t varies in the given interval. (For each answer, enter an ordered pair of the form x, y.) x = 1 + sin(t), y = 6 + 2 cos(t), π/2 ≤ t ≤ 2π The motion of the particle takes place on an ellipse centered at (x, y) = 1,6 . As t goes from π/2 to 2π, the particle starts at the point (x, y) = 1,6 and moves clockwise three-fourths of the way around the ellipse to (x, y) = .

Answer 1

Answer:

It moves clockwise three-fourths of the way around the

ellipse to (x, y) = (1,8)

Step-by-step explanation:

According to the information of the problem

$x = 1+\sin(t)\\y = 6+2\cos(t)$

for   $\frac{\pi}{2} \leq t \leq 2\pi$

For   $t = \pi/2$  the initial point is (x,y) = (1,6)  and for $t = 2\pi$

$x = 1 + \sin(2\pi) = 1\\y = 6 + 2\cos(2\pi) = 6+2 = 8$

therefore it moves clockwise three-fourths of the way around the

ellipse to (x, y) = (1,8)