Purpose
Return value
Syntax
=TANH(number)- number - The input number.
How to use
The TANH function returns a number's hyperbolic tangent. Given input -2, the function returns the number -0.96402758 as output.
=TANH(-2) // returns -0.96402758
Explanation
Just like the circular tangent, the hyperbolic tangent is defined in terms of the hyperbolic sine and hyperbolic cosine.
=SINH(a)/COSH(a) // definition of TANH(a)
Geometrically, the hyperbolic tangent of a number can be interpreted as the slope of the line from the origin to the point on the unit hyperbola corresponding to the number's hyperbolic angle where the hyperbolic angle is half the area under the hyperbola between the origin and that point.
For example, given the input of -1 the function returns -0.761594156.
=TANH(-1) // returns the slope of -0.761594156
This value can be interpreted as the slope of the line from the origin to the point corresponding to the hyperbolic angle of -1.
Plot of TANH
The plot of the hyperbolic tangent is shown below and visualizes the range of possible output of the function.
Images courtesy of wumbo.net.
Related functions
COSH Function
The Excel COSH function returns the hyperbolic cosine of a number.
SINH Function
The Excel SINH function returns the hyperbolic sine of a number.
TAN Function
The Excel TAN function returns the tangent of the angle given in radians. To supply an angle to TAN in degrees, multiply the angle by PI()/180 or use the RADIANS function to convert to radians.
ATANH Function
The Excel ATANH function returns the inverse hyperbolic tangent of a number.
