In this video I go over another example on graphing parametric equations and this time look at the equations x = sin(t) and y = sin²(t). The first thing to notice when looking at these parametric equations is that y = x² which is a simple parabola. But the domain and range of the parametric equations must also be taken into account when sketching the curve. Although the shape is a parabola we must look at the nature of the parametric equations to see how the path is traced along the curve. Since the parametric equations are trigonometric functions, they fluctuate periodically. Thus the path traced is a parabola but that moves back and forth along it an infinite amount of times.

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Example: Sketch the curve with the following parametric equations:

But since sin t is periodic then the point (x, y) = (sin t, sin²t) moves back and forth infinitely amount of times along the parabola from (-1, 1) to (1, 1) and vice-versa.