How do you sketch the curve with parametric equations $x = sin (t)$ $x = sin(t)$ , $y = {sin}^{2} (t)$ $y=sin^2(t)$ ?

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Answer 1 · 2014-10-05T14:17:16

Since we know that $- 1 \leq sin t \leq 1$ $-1 le sint le 1$ , the curve is limited to $- 1 \leq x \leq 1$ $-1 le x le 1$ .

By plugging $x = sin t$ $x=sint$ into $y = {sin}^{2} t$ $y=sin^2t$ , we have

$y = {(sin t)}^{2} = x^{2}$ $y=(sint)^2=x^2$ .

Hence, the curve is the portion of the parabola $y = x^{2}$ $y=x^2$ between $x = - 1$ $x=-1$ and $x = 1$ $x=1$ , which looks like this:

enter image source here

I hope that this was helpful.

How do you sketch the curve with parametric equations x=sin(t)x = sin(t), y=sin2(t)y=sin^2(t) ?