hyperbolic tangent function

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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 1

#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;
}

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 ( &infin; ) returns 1.

See Also

acos, asin, atan, atan2, cos, cosh, sin, sinh, tan

Standards

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