# Homework Help: Ellipse and a sine curve

1. Oct 23, 2007

### ehrenfest

1. The problem statement, all variables and given/known data
an ellipse whose semi axes have lengths a and b rolls without slipping on the curve y =c sin (x/a), find the relationship between a, b, and c. Assume that the ellipse completes one revolution per period of the sine curve.

The answer is b^2 = a^2 + c^2 and you find it by requiring that the arclengths be the same for one period.

Why is it wrong to just require that a = c and b = pi a /2 ? That would seem natural to me because then one half of the ellipse would fit perfectly into one "hump" of the sine curve?

2. Relevant equations

3. The attempt at a solution

Last edited: Oct 23, 2007
2. Oct 23, 2007

### ehrenfest

do people understand the problem?

3. Oct 23, 2007

### ehrenfest

should I draw a picture?

4. Oct 23, 2007

### Dick

An ellipse does not fit perfectly into a sine curve. I don't know what you are talking about.

5. Oct 23, 2007

### ehrenfest

My approach was to make the ellipse have minor axis equal to half the period of the sine curve and a semi-major axis equal to the amplitude of sine curve. All I want to know is why that approach produces ellipses that are different from the ones in the answer.

6. Oct 23, 2007

### Dick

Because they don't fit. The profile of an ellipse only resembles a sine curve. It's not an exact match.

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