## 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

1. 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|

2. 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

3. 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)

4. anonymous

I see. Cheers.