tanh

Hyperbolic tangent function

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Contents

Interface
Description
Special Values
See Also
Standards
Page Comments

Interface

#include <math.h>double  tanh (double x)
long  tanhl (long double x)
float  tanhf (float x)

Description

The tanh function computes the hyperbolic tangent of x, which is given by:

$\mathrm{tanh}(x) := \frac{\mathrm{sinh}(x)}{\mathrm{cosh}(x)} = \frac{e^x - e^{-x}}{e^x + e^{-x}}$

(1)

Example:

Example - Hyperbolic tangent function

Workings

#include <math.h>
#include <stdio.h>
int main(void)
{
  double val = -1.0;
  do
  {
    printf("Hyperbolic tangent of %f is %f.\n", val, tanh(val));
    val += 0.1;
  }
  while(val <= 1.0);
 
  return 0;
}

Solution

Output:

Hyperbolic tangent of -1.000000 is -0.761594.
Hyperbolic tangent of -0.900000 is -0.716298.
Hyperbolic tangent of -0.800000 is -0.664037.
Hyperbolic tangent of -0.700000 is -0.604368.
Hyperbolic tangent of -0.600000 is -0.537050.
Hyperbolic tangent of -0.500000 is -0.462117.
Hyperbolic tangent of -0.400000 is -0.379949.
Hyperbolic tangent of -0.300000 is -0.291313.
Hyperbolic tangent of -0.200000 is -0.197375.
Hyperbolic tangent of -0.100000 is -0.099668.
Hyperbolic tangent of -0.000000 is -0.000000.
Hyperbolic tangent of 0.100000 is 0.099668.
Hyperbolic tangent of 0.200000 is 0.197375.
Hyperbolic tangent of 0.300000 is 0.291313.
Hyperbolic tangent of 0.400000 is 0.379949.
Hyperbolic tangent of 0.500000 is 0.462117.
Hyperbolic tangent of 0.600000 is 0.537050.
Hyperbolic tangent of 0.700000 is 0.604368.
Hyperbolic tangent of 0.800000 is 0.664037.
Hyperbolic tangent of 0.900000 is 0.716298.
Hyperbolic tangent of 1.000000 is 0.761594.

Special Values

tanh ( 0 ) returns 0.

tanh ( ∞ ) returns 1.

Standards

The tanh function conforms to ISO/IEC 9899:1999(E).

Page Comments

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double	`tanh` (double x)
long	`tanhl` (long double x)
float	`tanhf` (float x)