Tanh

Syntax:

TANH(number)

• number: The numeric value for which you want to calculate the hyperbolic tangent.

Description:

The TANH function returns the hyperbolic tangent of a given number. The formula for the hyperbolic tangent is defined as:

TANH(number) = (e^number - e^(-number)) / (e^number + e^(-number))

Where e is the base of the natural logarithm (approximately 2.71828182845905). The result of TANH is a value between -1 and 1.

Examples:

1. =TANH(0) would return 0, as the hyperbolic tangent of 0 is 0.
2. =TANH(1) would return approximately 0.761594, based on the formula.
3. =TANH(-1) would return approximately -0.761594, as negative inputs result in negative outputs within the same range.
4. =TANH(2) would return approximately 0.964028, because the hyperbolic tangent approaches 1 as the input grows larger.
5. =TANH(-2) would return approximately -0.964028, as the hyperbolic tangent approaches -1 for large negative inputs.

Notes:

• The TANH function is often used in mathematical, engineering, or scientific calculations involving hyperbolic functions.
• The hyperbolic tangent is analogous to the TAN (tangent) function but relates to hyperbolic geometry.
• As the input moves towards infinity in the positive or negative direction, the result of TANH converges towards 1 or -1, respectively.
• The function accepts both positive and negative numeric inputs, including zero.