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Question

Describe the motion of a particle with position (x, y) as t varies in the given interval.

20. x = 2 + sin t, y = 1 + 3 cos t, π/2 ≤ t ≤ 2π

Solution Preview

Calculations:

The parametric equation for x is as below.

x = 2 + sin t

sin t = x 2 ( 1 )

The parametric equation for y is as below.

y = 1 + 3 cos t

cos t = y 1 3 ( 2 )

Squaring and adding equations (1) and (2) to obtain the equation of motion of the particle, we get,

sin 2 t + cos 2 t = 1 ( x 2 ) 2 + ( y 1 3 ) 2 = 1

...

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