Find parametric equations that describe the circular path of the following object. assume (x, y) denotes the position of the object relative to the origin at the center of the circle. use the units of time given in the description. a go-cart moves clockwise with constant speed around a circular track of radius 600 m, completing one lap in 1.8 min.

  (x, y) = (600cos(10πt/9), -600sin(10πt/9))

Step-by-step explanation:

The usual translation between rectangular and polar coordinates is ...

Here, the radius is constant at r = 600 m, and the angle changes linearly with time. If we assume the initial angle is 0, then it is -2π radians (one full turn clockwise) at t=1.8 minutes. The relationship between θ and t will be given by ...

  θ = (-2π)(t/1.8) = -10πt/9

Using these values for r and θ, we get the parametric equations ...

We can take advantage of the fact that cosine is an even function, so cos(-θ) = cos(θ), and that sine is an odd function, so sin(-θ) = -sin(θ). This lets us write the equations as ...

  (x, y) = (600·cos(10πt/9), -600·sin(10πt/9))

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