Finding the Area Under One Arch of a Cycloid: Where to Start?

[mmont012]

Homework Statement

Find the area under one arch of the cycloid
x=a(t-sint), y=a(1-cost)

Where do I start?

I could divide both sides by a and get
x/a= t-sint cost=1-y/a

If this is the case, how should I deal with x/a=t-sint? I need to get them into the form of sint=... or cost=... right?

 

[SteamKing]

Homework Statement

Find the area under one arch of the cycloid
x=a(t-sint), y=a(1-cost)

Where do I start?

I could divide both sides by a and get
x/a= t-sint cost=1-y/a

If this is the case, how should I deal with x/a=t-sint? I need to get them into the form of sint=... or cost=... right?

First, don't panic.

Second, don't do anything to the original parametric equations to make them unsuitable for finding the area under the curve.

Third, how do you find the area under any given curve? What integral expression would you write? What does this integral expression look like after you substitute the parametric expressions for x and y?

 

[mmont012]

(taking deep breaths)...

Can I use the ∫(from α to β) of 1/2 r²?

I also have the relationships: x=rcosθ and y=rsinθ

Since my parametric equation is in terms of t am I able to say x=rcost and y=rsint?

 

[LCKurtz]

(taking deep breaths)...

Can I use the ∫(from α to β) of 1/2 r²?

I also have the relationships: x=rcosθ and y=rsinθ

Since my parametric equation is in terms of t am I able to say x=rcost and y=rsint?

No. Those are parametric equations alright, but they are not polar coordinate equations just because they have sines and cosines. Look at SteamKing's post #2. To help you, you should be able to find a couple of $t$ values where $y=0$. That should help you find one arch of the cycloid.