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anonymous
 one year ago
Lecture 5  Parametric equations
Hi,
When the cycloid is first introduced, the position of a point, P, on the circumference is described as (all the following are vectors)
OP = OA + BA + BP
BP = < asinTheta, acosTheta >
I don't understand this as I thought
x = rcosTheta
y = rsinTheta
Therefore should the components of BP be,
BP = < acosTheta, asinTheta >?
Thanks
anonymous
 one year ago
Lecture 5  Parametric equations Hi, When the cycloid is first introduced, the position of a point, P, on the circumference is described as (all the following are vectors) OP = OA + BA + BP BP = < asinTheta, acosTheta > I don't understand this as I thought x = rcosTheta y = rsinTheta Therefore should the components of BP be, BP = < acosTheta, asinTheta >? Thanks

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phi
 one year ago
Best ResponseYou've already chosen the best response.2yes, for a circle centered at the origin, and measuring theta counterclockwise from the xaxis, then the points on it circumference have coords \[ x= r \cos \theta \ , y= r \sin \theta \] but in this problem, the angle is measured in a "nonstandard" way. specificially dw:1440521647396:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Hello Phi, Thanks for replying so quickly. So essentially when going clockwise sin and cos give the opposite coordinates to what they give when going anticlockwise? Thanks

phi
 one year ago
Best ResponseYou've already chosen the best response.2the other difference is we are measuring theta from the line pointing straightdown (i.e. parallel to the negative yaxis). this switches which "leg" is sin and cos (as compared to using the positive xaxis as the start)
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