The position of an object in circular motion is modeled by the given parametric equations. Describe the path of the object by stating the radius of the circle, the position at time t = 0, the orientation of the motion (clockwise or counterclockwise), and the time t that it takes to complete one revolution around the circle. x = 2 sin(t), y = 2 cos(t)

Question
Asked Nov 3, 2019
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The position of an object in circular motion is modeled by the given parametric equations. Describe the path of the object by stating the radius of the circle, the position at time t = 0, the orientation of the motion (clockwise or counterclockwise), and the time t that it takes to complete one revolution around the circle.
x = 2 sin(t), y = 2 cos(t)

check_circle

Expert Answer

Step 1

The two parametric equations are, x=2sint and y=2cost

For calculating the radius of the circle, we use the formula,

|x2 +y
r =
(2 sin t) +(2 cost)
=4 sin2 t+4 cos't
2/sin2tcos2t
2
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|x2 +y r = (2 sin t) +(2 cost) =4 sin2 t+4 cos't 2/sin2tcos2t 2

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Step 2

Position of the object at a given time t=0 is (0,2)

x 2 sin
2 sin(0) = 0
y 2 cost 2 cos(0) 2
Hence (x,y) (0,2)
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x 2 sin 2 sin(0) = 0 y 2 cost 2 cos(0) 2 Hence (x,y) (0,2)

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Step 3

Orientation of the object;

Substitute x= π/2 and π and check the corresponding value for x.

  • If the value for x decreases for increasing values of t, then t...
x 2 sin
x 2 sin( 0
As the value of x decreases for increasing values of t, the orientation is anti clockwise
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x 2 sin x 2 sin( 0 As the value of x decreases for increasing values of t, the orientation is anti clockwise

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Math

Calculus

Functions