Simple question: I've been asked find a parameterization of the circle of radius $2$ starting at $(2,0)$, moving in the counterclockwise direction.
Simple enough I get $(2\cos(t),2\sin(t))$ because $x=r\cdot \cos \theta$ and $y=r\cdot \sin \theta$.
Now the second part of the question asks the same but in the clockwise direction and the answer provided is $(2\sin(t),2\cos(t))$. I don't understand how this is possible.
If we take $t$ as $-t$ because of the opposite direction it still only makes sense to say the parameterized equation is $(2\cos(t),-2\sin(t))$. And I don't see how for the $x$ - coordinate we can have
$$ x= r\cdot \sin (t)$$ and similarly for the $y$ - coordinate
$$ y= r\cdot \cos (t)$$
We never covered parametric equations in Calc II and because I'm in a different school, it's assumed(rightly) that we know parametric equations.
Thanks in advance.