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Question

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

21. x = 5 sin t, y = 2 cos t, −π ≤ t ≤ 5π

Solution Preview

Calculations:

The parametric equation for x is as below.

x = 5 sin t

sin t = x 5 ( 1 )

The parametric equation for y as below.

y = 2 cos t

cos t = y 2 ( 2 )

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

sin 2 t + cos 2 t = 1 ( x 5 ) 2 + ( y 2 ) 2 = 1

The value of t is increased from π to 5 π .

Let us substitute the values of t in the parametric equations x = 5 sin t and y = 2 cos t to obtain the value of x and y respectively...

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