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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Example: What curve is represented by the following parametric equations?
Also from Example 2, https://youtu.be/SBkzZDlqTTE, the parametric equations x = cos(t), y = sin(t) gave the exact same curve, which is a unit circle!
But notice how the points are traced as we increase t from 0 to 2π.
In example 2, the curve is traced by starting at the point (1, 0) and rotating counterclockwise around the circle once.
But in this example the same curve is traced by starting at the point (0, 1) and rotating clockwise around the circle twice.
Thus examples 2 and 3 show that different sets of parametric curves can represent the same curve.
Thus, we distinguish between a curve, which is a set of points, and a parametric curve, in which the points are traced in particular way.
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