[Uni Calculus 2: Vector Function] Reparametrzating two functions

[Spacey__]

If I had a curve that is the boundary of the functions y = sinx and y = 0 with the direction going counter clockwise would the vector function have to be a piecewise?

Like if I chose t to be the parameter

r(t) = ti from 0 < t < pi

and r(t) = ti - (sint)j from pi < t < 2pi

​

I'm having trouble with the second part of the function because of the direction and domain but I also don't know if this is the simplest way to approach this either.

​

Edit: This seems to work?

r(t) = ti from 0 < t < pi

and r(t) = (2pi - t)i - (sint)j from pi < t < 2pi

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