STuck? if cartesian equation of x= sint, y=cos^2t is = x^2 + y = 1... how does the graph in the range of -2pi

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STuck? if cartesian equation of x= sint, y=cos^2t is = x^2 + y = 1... how does the graph in the range of -2pi

Mathematics
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is you r question, the graph being a parabola or having a range beyond -1 and 1?
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So am I trying to graph with incorrect points or is my graph correct?

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yes its clear that x can only take values between -1 and 1 since \(-1\leq \sin(t) \leq 1\) so your graph is correct
so if my professor asked me to identify the behavior of the graph according to the cartesian equation I derived from these x and y functions... I could tell him that a particle traveling along the path of this graph would actually travel clockwise then bounce back and travel counterclockwise between the -1 and 1 on the x-axis..???? does that make sense?
because thats' mainly my thing, Im trying to understand the behavior of how a particle would travel along this path. starting at -2pi and ending at 2pi.. and since my graph starts and ends at -1 and 1... would my conclusion be correct? (about the bouncing back and forth)
are you still there?
yes the idea of travelling is derived from the time - t So if we take the distance on x direction, the relationship of that with the time is given as \(x = \sin(t)\) so there itself it says that the x change in a oscillatory way
ok. fantastic!!!!!!! thank you. I just wanted to make sure I was on the right track. And you seem pretty confident. :) Thank you very much.
you are welcome
here what desmos.com give
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