KermMartian at 19:15, 24 February 2016

2016-02-24T19:15:04Z

← Older revision		Revision as of 19:15, 24 February 2016
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	The tanh( command can be used to approximate the sign function:		The tanh( command can be used to approximate the sign function:

	~~[[TI-BASIC:Math\|Math]]~~		<math>
	\operatorname{sgn} x=\begin{cases}-1&\text{if }x<0,\\0&\text{if }x=0,\\1&\text{if }x>0.\end{cases}		\operatorname{sgn} x=\begin{cases}-1&\text{if }x<0,\\0&\text{if }x=0,\\1&\text{if }x>0.\end{cases}
	~~[[TI-BASIC:~~/math~~\|/math]]~~		</math>

	As the absolute value of the input becomes large, the convergence is achieved at a point closer to zero. For the function to work as intended generally, numbers having lesser orders of magnitude need to be multiplied by a factor large enough for the argument to arrive at ±16.720082053122, which is the smallest input to produce ±1 (respectively) to fourteen digits of accuracy.		As the absolute value of the input becomes large, the convergence is achieved at a point closer to zero. For the function to work as intended generally, numbers having lesser orders of magnitude need to be multiplied by a factor large enough for the argument to arrive at ±16.720082053122, which is the smallest input to produce ±1 (respectively) to fourteen digits of accuracy.
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	The definition of the hyperbolic tangent is:		The definition of the hyperbolic tangent is:
	~~[[TI-BASIC:Math\|Math]]~~		<math>
	\tanh{x}=\frac{e^x-e^{-x}}{e^x+e^{-x}}=\frac{e^{2x}-1}{e^{2x}+1}		\tanh{x}=\frac{e^x-e^{-x}}{e^x+e^{-x}}=\frac{e^{2x}-1}{e^{2x}+1}
	~~[[TI-BASIC:~~/math~~\|/math]]~~		</math>

	= Related Commands =		= Related Commands =
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	* [[TI-BASIC:Cosh\|Cosh(]]		* [[TI-BASIC:Cosh\|Cosh(]]
	* [[TI-BASIC:Arcosh\|coshֿ¹(]]		* [[TI-BASIC:Arcosh\|coshֿ¹(]]
	* [[TI-BASIC:Artanh\|tanhֿ¹(]][[Category:TI-BASIC]]		* [[TI-BASIC:Artanh\|tanhֿ¹(]]
			[[Category:TI-BASIC]]
	[[Category:TIBD]]		[[Category:TIBD]]

Maintenance script: Initial automated import

2016-02-24T18:08:42Z

Initial automated import

New page

{{Template:TI-BASIC:Command
|picture=TANH.GIF
|summary=Calculates the hyperbolic tangent of a value.
|syntax=tanh(''value'')
|location=The tanh( command is only found in the Catalog. Press:
# 2nd CATALOG to access the command catalog.
# T to skip to commands starting with T.
# Scroll down and select tanh(.
|compatibility=TI-83/84/+/SE
|size=1 byte
}}

Calculates the hyperbolic tangent of a value. The hyperbolic trig functions [[TI-BASIC:Sinh|Sinh(]], [[TI-BASIC:Cosh|Cosh(]], and tanh( are an analog of normal trig functions, but for a hyperbola, rather than a circle. They can be expressed in terms of real powers of [[TI-BASIC:E_Value|e]], and don't depend on the [[TI-BASIC:Degree_Mode|Degree]] or [[TI-BASIC:Radian_Mode|Radian]] mode setting.

tanh(0)
0
tanh(1)
.761594156

Like normal trig commands, tanh( works on lists as well, but not on complex numbers, even though the function is often extended to the complex numbers in mathematics.

= Advanced Uses =

The tanh( command can be used to approximate the sign function:

[[TI-BASIC:Math|Math]]
\operatorname{sgn} x=\begin{cases}-1&\text{if }x<0,\\0&\text{if }x=0,\\1&\text{if }x>0.\end{cases}
[[TI-BASIC:/math|/math]]

As the absolute value of the input becomes large, the convergence is achieved at a point closer to zero. For the function to work as intended generally, numbers having lesser orders of magnitude need to be multiplied by a factor large enough for the argument to arrive at ±16.720082053122, which is the smallest input to produce ±1 (respectively) to fourteen digits of accuracy.

5/12→X
.4166666667
tanh(E9X)
1
tanh(-E9X)
-1

= Formulas =

The definition of the hyperbolic tangent is:
[[TI-BASIC:Math|Math]]
\tanh{x}=\frac{e^x-e^{-x}}{e^x+e^{-x}}=\frac{e^{2x}-1}{e^{2x}+1}
[[TI-BASIC:/math|/math]]

= Related Commands =

* [[TI-BASIC:Sinh|Sinh(]]
* [[TI-BASIC:Arsinh|sinhֿ¹(]]
* [[TI-BASIC:Cosh|Cosh(]]
* [[TI-BASIC:Arcosh|coshֿ¹(]]
* [[TI-BASIC:Artanh|tanhֿ¹(]][[Category:TI-BASIC]]
[[Category:TIBD]]

TI-BASIC:Tanh - Revision history

KermMartian at 19:15, 24 February 2016

Maintenance script: Initial automated import