Question

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

Answer 1

Since we know that `-1 le sint le 1`, the curve is limited to `-1 le x le 1`.

By plugging `x=sint` into `y=sin^2t`, we have

`y=(sint)^2=x^2`.

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

I hope that this was helpful.