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

[Poetria]

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. :(

 

[Orodruin]

Those parametrizations are just different parametrizations of the unit circle.

 

[FactChecker]

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.

 

[Poetria]

Those parametrizations are just different parametrizations of the unit circle.

Ok, I got it. Many thanks. But why is my answer wrong then?

 

[Poetria]

Great, I understand everything now. Many thanks.

 

[vela]

Ok, I got it. Many thanks. But why is my answer wrong then?

Hard to say because you never told us what the question actually was!

 

[Poetria]

"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.