Please look at this webpage for reference: http://mathworld.wolfram.com/Hypocycloid.html
Go to line 7 to 15 on that webpage. Line 7 and 8 show 2 parametric equations. These have been rewritten as in line 12 and 13. I understand how this has been done. But I want to know how these parametric equations (line 12 and 13) have been used to get the arc length and the area equations (line 14 and 15 respectively).
I have tried using the arc length formula:
I rearranged to get the radius in terms of S and theta. Then I substitute that into the area equation:
But that gives me the area in terms of theta. However, on the webpage, there is no angle or theta.
How should I do this? If there is something I am mission or these is another, better way to do this, please tell me.
Sorry for my incompetence and thanks in advance.
By "LINE" I mean the numbers that are on the right side of the page in brackets