help please :(((( supposed to find cartesian equation for x = sin t and y = cos^2 t ... in the range -2pi

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help please :(((( supposed to find cartesian equation for x = sin t and y = cos^2 t ... in the range -2pi

Mathematics
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x = sin t y = cos^2 t x^2 + y = ?
1
Now I do understand that equation and when I try to plot points on my graph I end up with a semi circle in quadrant 1 and 2 along the x-axis, but I don't understand what the behavior would be if it's a semi circle, would a particle only be traveling along the half circle from -1 to 1 and then make another loop ? or is the direction assuming two passes along the semi circle.?

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do you really think \(x^2+y=1\) is a circle ?
no, but Im confused because the range is supposed to be from -2pi to 2pi?
Maybe forget about range for now what do you know about the graph of \(x^2+y=1\) ?
that x^2 is a parabola and y would be a horizontal shift
right, try sketching the graph
Got it. Thank you
what about range ?
if it helps, split the given range of \(t\) into multiple intervals like : (0, pi/2) (pi/2, pi) (pi, 3pi/2) (3pi/2, 2pi) and see what part of the graph gets traced in each interval
I'm sorry to bother you but I am still having a bit of trouble, I thought I figured it out, but Im still stuck. :(

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