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How to I make arctrig functions grow arbitrrily large while they maintain cyclical properties?


MWresearch
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I'm running into a problem where I want to represent a series of radians as A*arccos(Bx+C)+D, like for instance pi/2, 3*pi/4, pi...18*pi/12.. or pi/2, pi, 3pi/2, 2pi, pi/2, pi, 3pi/2....ect. But, because the domain of arccos is limited and then becomes some imaginary hyperbolic trig function outside of the domain 0<x<pi, I'm having trouble figuring out how to do that. Like normally, you could represent a series of cyclical numbers like 1,-1,1,-1 as cos(pi*x). I want to do the same thing with radians using arccos(x) where it just keeps repeating periodically as x grows arbitrarily large

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I don't know what you mean exactly, but it could lead to the right idea. If you increase by a smaller and smaller number that never increases past pi, then arccos should grow indefinitely large, but it does so logarithmically according to the hyperbolic trig function so it's still not cyclical. the only thing I could think that works is arccos(cos(pi*x))*pi or something like that, but I never see anything like that anywhere.

Edited by MWresearch
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I don't know what you mean exactly, but it could lead to the right idea. If you increase by a smaller and smaller number that never increases past pi, then arccos should grow indefinitely large, but it does so logarithmically according to the hyperbolic trig function so it's still not cyclical. the only thing I could think that works is arccos(cos(pi*x))*pi or something like that, but I never see anything like that anywhere.

 

It will convert arbitrary values into the range arccos is looking for.

 

123456 / 106 = 0.123456

-123 / 103 = -0.123

 

# of Digits to left of decimal = ⌊log10(|x|)⌋+1

 

arccos(x / 10⌊log10(|x|)⌋+1 )

Edited by Endy0816
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