Parametric Curves: Example 3: Unit Circle

In this video I go over another example on parametric curves and this time graph the curve formed from the parametric equations x = sin(2t) and y = cos(2t). This is very similar to the parametric equations in example 2, and in fact they both represent the exact same curve, which is a unit circle! But the only difference is that the path or route that is traced is in a different method. In example 2 the path traced is by first starting at the point (1, 0) and then rotating counterclockwise once to form a circle. But in this example the path is traced by starting at the point (0, 1) and rotating clockwise twice to form a circle. Thus we should distinguish between a curve, which is set of points, and a parametric curve, which is the particular path that a particle travels. This is a very interesting example on how different parametric equations can represent the same curve, albeit different paths taken, so make sure to watch this video!

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I don't always graph parametric curves but when I usually get the same curve as other parametric equations ;)


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