How can I accurately model a sine wave using popsicle sticks?

[Hornbein]

I'm making a model of a sine wave out of popsicle sticks. Essentially I'm digitizing a sine wave.

Let's say I'm modeling half of a cycle with ten sticks. So I need to know how long to cut each stick. So I figured it would be cos(arcsin(x/10)) for x=0 through 9. Wrong! I still can't figure out what the problem is, so I printed out a sine wave and traced it onto the sticks. That worked, of course.

 

[Khashishi]

I don't know where you come up with such a complex formula. Try sin((pi*(n-1))/9)

 

[Hornbein]

The sticks are horizontal, aligned with the X axis.

 

[berkeman]

The sticks are horizontal, aligned with the X axis.

Can you post a sketch of what you are tying to do? So far the explanation is confusing (at least to me)...