Suppose the motion of a particle is given by

x = 4 cos t, y = sin t.

1. Describe the motion of the particle, and sketch the curve along which the particle travels.

quilly Apr 15, 2018

#1**+1 **

x = 4cos t ⇒ x/4 = cos t

y = sin t

So...using cos^2 t + sin^2 t = 1, we have

(x/4)^2 + y^2 = 1

x^2 / 16 + y^2 = 1

This is an ellipse

When t = 0 we have (4,0)

When t = pi/2 we have (0, 1)

When t = pi we have (-4, 0)

When t = 3pi/2 we have (0, -1)

When t 2pi we have (4, 0)

So....the curve is traced out in a counter-clockwise direction

Here's the graph : https://www.desmos.com/calculator/yscc2qxqsk

CPhill Apr 15, 2018