Position vectors as a function of time
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For the position vector:
\[
r(t) = -2 \cos \left(\frac{\pi t}{2}\right) i + 2 \sin \left(\frac{\pi t}{2}\right) j, \; t \geq 0
\]
i) Find the cartesian equation that represents the path of the particle.
ii) Find its domain and range.
iii) Sketch the graph.
iv) Give the starting point of the particle's motion, the direction of the motion, and the period of motion.
i) \(x^2+y^2=4\)
ii) Domain \([-2,2]\), Range \([-2,2]\)
iii) Refer to worked solution
iv) Starts at \((-2,0)\), moves clockwise with a period of \(4\).
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