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- anonymous

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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- anonymous

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- phi

yes, for a circle centered at the origin, and measuring theta counter-clockwise from the x-axis, 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 "non-standard" way.
specificially
|dw:1440521647396:dw|

- anonymous

Hello Phi,
Thanks for replying so quickly.
So essentially when going clockwise sin and cos give the opposite coordinates to what they give when going anti-clockwise?
Thanks

- phi

the other difference is we are measuring theta from the line pointing straight-down (i.e. parallel to the negative y-axis). this switches which "leg" is sin and cos (as compared to using the positive x-axis as the start)

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- anonymous

I see. Cheers.

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