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# Tan and tanh function?

Hello,

I would like to use tanh function in a query. Like
SELECT column1, tanh(column2) from table1

However tanh is not know to sql server. Does somebody has a solution?

Regards,
Dennis
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Schuttend
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1 Solution

Billing EngineerCommented:
what IS the tanh function doing?

sql server has ATAN:
http://msdn.microsoft.com/en-us/library/ms181746.aspx
and ATN2:
http://msdn.microsoft.com/en-us/library/ms173854.aspx

...
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Author Commented:
tanh squashes a signal so that the value is always between -1 and 1. Both tanh and atn2 are doing something else...
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Billing EngineerCommented:
well, COS and SIN function also return values between -1 and +1 ...
but sure that's not what you are looking for.
I am not a advanced math guy, so I don't know what/how the tanh function is working. I can only work with a proper formula, and translate that into either some sql code using the existing functions, or suggest to get it into a sql 2005 clr function (using c# code)...

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Commented:
TanH is hyperbolic tangent,
and can be approximated by
tanh(a) = [exp(a) - exp(-a)]/[exp(a) + exp(-a)],
where a is an angle in radians (i.e. between 0 and 1)
http://en.wikipedia.org/wiki/Hyperbolic_tangent
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Commented:
Oops - a radian doesn't have to be between 0 and 1
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Commented:
Schuttend:

The hyperbolic tangent (TANH) function is the hyperbolic sin / the hyperbolic cosine.  You can work up functions for SINH, and COSH, and then one for TANH.  The formula's are:

SINH = (e^x - e^-x) / 2

COSH =  (e^x + e^-x) / 2

Where x is the angle in radians.  Your hyperbolic tangent function is then:

TANH = SinH / CosH
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Author Commented:
you are indeed correct,its the hyperbolic tangent, but how can I insert this in a query? What would be the correct format?

regards,
Dennis
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Commented:
I believe you can write functions in SQL Server.  These functions can then be used in your query.
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Billing EngineerCommented:
that gives me the input I need:
``````declare @x float
declare @sinh float
declare @cosh float
set @x = 0.14
select @sinh = (power( exp(1), @x ) - power ( exp(1), -@x) / 2)
, @cosh = (power( exp(1), @x ) + power ( exp(1), -@x) / 2)
select @x x , @sinh sinh, @cosh cosh, @sinH/@cosh tanh
``````
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Commented:
You needn't create separate SINH and COSH functions if you only need TANH in one query, simply

select (exp(myAngle) - exp(-myAngle)) / (exp(myAngle) + exp(-myAngle) As TANH
from ...
assuming you are able to select the angle from a table in radians (not degrees).
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Commented:
GO-87:

I realize the SinH and CosH functions weren't absolutely necessary and it could have been done "in line".  Since the Hyperbolic Tangent is actually the Hyperbolic Sin divided by the Hyperbolic Cos, having those two functions may be useful in the future, and makes the coding of the TanH function clearer and in the format that would be recognized easiest as SinH / CosH.

To convert degrees to radians you must multiply:

Radians = Degrees * (pi / 180)
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Commented:
AielloJ:
No worries, I wasn't implying any criticism, actually I agree with you.
In fact, had I seen angelIII's post (which came in while I was typing), I wouldn't have commented at all.
It's been many years since I've had to think about tanh ... and series and such things.
Cheers
G
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Commented:
GO-87:

No offense taken.  I'm a big fan of structure and reusability.  If Schuttend needs sTanH, he or she will probably need SinH and CosH one day as well, as well as conversions from degrees to radians.  Just thought I'd structure my answer that way up front.

Likewise on the math... It's been awhile, and an interesting challenge recalling it.  Glad we came up with the same algorithm.  LOL
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Commented:
:-)
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