# Hi, I have been trying to understand the derivation of a hypocycloid's parametric equation, but am stuck with one part.

I have been using someone else's answer on the same site to understand the problem: here's the link - Parametric equations for hypocycloid and epicycloid

I can understand everything but the part where it says - "The coordinate of the moving point $P$ relative to $B$ are: $bcos(ϕ),−bsin(ϕ)$, where the minus sign is due to the fact that $ϕ$ is measured clockwise." Okay so I am assuming that because the circle moves in a clockwise direction my y value decreases while my $x$ value is increasing, so that's why the $y$ value is negative.

But if my understanding is right, then if we consider the smaller circle revolving around the bigger circle, in that part as well, shouldn't my coordinates for smaller circle have a negative $x$ value and a positive $y$ value (because here $x$ value is decreasing, while $y$ is increasing)?

What am I getting wrong?

I have tried looking it up other websites as well, but nothing helps. I am really confused so if anyone could help, it would be really appreciated.

Thanks a lot :)

• WELCOME to Math SE! Please try to limit the number of things you ask in this question. There are probably six questions in the problem which will make what you're asking for extremely vague. – KingDuken Jul 14 '16 at 14:12
• Thanks! ive cut down my questions.. – paul Jul 15 '16 at 1:39
• The point is, if you consider a moving coordinate system with origin at $B$, then $P$ travels clockwise around $B$, assuming $B$ travels counterclockwise around the inside of the larger circle. – Andrew D. Hwang Jul 15 '16 at 1:44