Parametrised Circle Trajectory: Particle in x≤0 Half-Plane

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Homework Statement
There is a unit circle, where x(t)=sin(t), y(t)=cos(t)
0≤t<pi
Relevant Equations
x^2+y^2=1
The trajectory of a particle is a semi-circle contained in the x≤0 half-plane.

Well, this is somewhat weird. I have come across examples with x(t)=cos(t), y(t)=sin(t) and not the other way round.
By the way, my answer is wrong but I don't know why. This is probably silly. :(
 
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Those parametrizations are just different parametrizations of the unit circle.
 
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Those are actually different paths going in different directions. For ##t \in (0,\pi)##, (cos(t),sin(t)) stays in the upper half-plane and goes counter-clockwise from (1,0) to (-1,0). The counter-clockwise, starting at (1,0), parameterization occurs often in complex analysis and elsewhere, but usually goes all the way around the circle.
(sin(t),cos(t)) stays in the right half-plane, starts at (0,1) and goes in a clockwise direction to (0,-1). That is an unusual parameterization.
When line integrals are studied, the correct direction of the path is critical. And the ends of the paths are always critical.
 
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Orodruin said:
Those parametrizations are just different parametrizations of the unit circle.
Ok, I got it. Many thanks. But why is my answer wrong then? :rolleyes:
 
Great, I understand everything now. Many thanks. 😍
 
Poetria said:
Ok, I got it. Many thanks. But why is my answer wrong then? :rolleyes:
Hard to say because you never told us what the question actually was!
 
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"The trajectory of a particle is a semi-circle contained in the x≤0 half-plane." - this one is wrong. There were several options in this problem.
The right one: The trajectory of a particle is a semi-circle contained in the x≥0 half-plane.

Thank you very much. I know this is easy but I was confused.
 
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