# Length of Sine Curve

1. Apr 15, 2012

I tried to find the length of a sine curve using calculus.I got stuck in the integral of integral(sqrt(cos(x)^2+1), x, 0, a). Limits are from 0 to point a,i.e. length of curve from 0 to any point a.With some approximations I found out the length of sine curve as a result.I have attached the derivation of my result.I tried searching books and internet for this result.But couldn't find like this one.It also seems that this result gives more precise answer.

#### Attached Files:

• ###### Attempt to find length of sine curve from 0 to any a.pdf
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2. Apr 15, 2012

### chiro

3. Apr 16, 2012

I know elliptic integrals.It comes when you try to find time period of a simple pendulum without taking usual approximation:that angular displacement is very small and that
sin(θ)≈θ in radians.But even elliptical integrals can't be solved analytically.You have to solve it in a calculator/computer or use interpolation formula's to carry out integral approximately.However the method of approximation which I used gives a result which gives better answer compared to a calculator or interpolation.In the end of pdf I have given three checks of that result which I haven't seen anywhere.I have also searched the net extensively.That's why I posted here to ask you guys if it's a new result or not??

4. Apr 16, 2012

### chiro

I don't know if its a new result or not (hell I didn't know what an elliptic integral was!). Hopefully somebody else can give you a better answer.

5. Apr 16, 2012