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Tweaking my sin curve

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I have not done math in a while, so I cannot remember how I can achieve this, but this is what I want: I have a function that takes a value between 0 and 1. Here is my function currently: f(x) = (sin(x*PI - PI/2) + 1.0) / 2.0 This *almost* does what I want, since I want: f(x) to be 0 when x is 0 f(x) to be 0.5 when x is 0.5 f(x) to be 1 when x is 1 But I want the curve to go a bit differently. Here is the image of what I have, and what I want: Clicky The red line being the above function which I have, and the blue line being what I would like to have approximatly. Basically, I want the curve to be a bit shallower initially, then steeper suddenly. Can anyone tell me where I can put a variable in my current equation to get what I need? Many thanks!

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Your blue curve looks a bit like a shifted Langevin function.

http://scienceworld.wolfram.com/physics/LangevinFunction.html

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Quote:
Original post by Airo
Your blue curve looks a bit like a shifted Langevin function.

http://scienceworld.wolfram.com/physics/LangevinFunction.html


Yea, I think that would work to, but I went with sigmoid function; it seems just right.

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