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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
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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

 

 

cool cool cool

 
CPhill  Apr 15, 2018

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