How to obtain an equation for this grapgh?

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Homework Statement


i am doing my Honor project and i have obtained a graph like the picture below,now i must give an equation for this graph,any ideas how i can obtain an equation which is compatible with this graph?
thanks
 

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i have an idea about this,it seems they are like Cosine functions with different amplitudes,but what can be an equation for it?
 
Possibly. It might, for example, be y= aebxcos(cx). See if you can find a, b, and c by letting x and y be coordinates of three points on your graph. And then, check to see if they work for other points on the graph.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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