How do I parametrize half (upper part) of the unit circle clockwise? I tried with x=cos t, y= -sin t, pi<t<0. But something seems wrong. How do I think with “clockwise” and “upper part”? =)
x = cos t, y = sin t, and t going from pi to 0 is one way
x = sin t, y = cos t, and t going from -pi/2 to pi/2 is another way
If you are using y=-sin t, you cannot have 0<t<pi because sine is positive in 1st and second quadrant, your parametrization gives lower half of the circle
But won’t the circle take the “lower” part then? How does it know that it should go clockwise? I’ve hear that it takes the counter-clockwise way with the parametrization x=cos t, y=sin t.