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TANH function

Hyperbolic tangent function. TANH(x) returns the hyperbolic tangent of x. The argument x must be expressed in radians. To convert degrees to radians you use the RADIANS function. The result is in the range (−1, 1).

The hyperbolic tangent can be defined as:

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

The argument x can be a real number, a complex number, or a matrix. When it is a matrix, the function returns a matrix with the same dimensions and with the TANH function applied to all elements.

Examples

TANH(0) equals 0

TANH(1) equals 0.7615942

Calculator

TANH 0.761594155956

Graph

TANH function

Relation with COSH and SINH functions

Hyperbolic functions COSH, SINH, TANH

Related functions

  • ATANH function: Inverse hyperbolic tangent function
  • SINH function: Hyperbolic sine function
  • COSH function: Hyperbolic cosine function
  • RADIANS function: converts degrees into radians.
  • Hyperbolic functions

External links