Question

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

Answer 1

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