parameterization of a semicircle, clarification
The component of a (clockwise) semicircle and circle with radius 2 are the same, (2cos(t),2sin(t)). Is this because the semicircle is only defined in 0<= y <=2?
Original post by localmemelord
The component of a (clockwise) semicircle and circle with radius 2 are the same, (2cos(t),2sin(t)). Is this because the semicircle is only defined in 0<= y <=2?
It will be on a limited range of t, not necessarily starting at 0. Any arc of the circle can be specified with a limited range.
(edited 3 years ago)
Original post by RogerOxon
It will be on a limited range of t, not necessarily starting at 0. Any arc of the circle can be specified with a limited range.
oh ok, so the range would be 0<= t <= pi/2, right?
Original post by localmemelord
oh ok, so the range would be 0<= t <= pi/2, right?
No. t would need to vary by more than that. Can you see why?
Original post by RogerOxon
No. t would need to vary by more than that. Can you see why?
would that range only define a half of the semicircle, i.e. top right of the circle that is centred around the origin?
(edited 3 years ago)
Original post by localmemelord
would that range only define a half of the semicircle, i.e. top right of the circle that is centred around the origin?
Yes.
Original post by localmemelord
would that range only define a half of the semicircle, i.e. top right of the circle that is centred around the origin?
Yes. It's also the range of t that is important, not where it starts.
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