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Canuckish
 11 months ago
Determine if the following trajectory lies on a circle...
I start with a vector <sint+sqrt(3)cost, sqrt(3)sintcost>
I am down to 2(cos^2)t+4(sin^2)t+2sintcost2sqrt(3)sintcost but am just bad enough at trig to not know what to do from here to find what the radius is this trajectory lies on...
Canuckish
 11 months ago
Determine if the following trajectory lies on a circle... I start with a vector <sint+sqrt(3)cost, sqrt(3)sintcost> I am down to 2(cos^2)t+4(sin^2)t+2sintcost2sqrt(3)sintcost but am just bad enough at trig to not know what to do from here to find what the radius is this trajectory lies on...

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quekyuxuan
 11 months ago
Best ResponseYou've already chosen the best response.0Your algebra is wrong; if you square the formulas for x and y separately and add them, the sintcost terms will cancel, and you'll be left with 4(sin^2 t + cos^2 t), so the magnitude of your vector is constant for all values of t

phi
 11 months ago
Best ResponseYou've already chosen the best response.0you have a vector v= <x,y> where both x and y are functions of t the length of the vector is \[ \sqrt{v \cdot v} = \sqrt{x^2+y^2} \] if this length is constant then we know all the points traced out by v over time must lie on the circumference of a circle.
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