SECH function

The SECH function in Excel calculates the hyperbolic secant of a given number. The hyperbolic secant of $x$ is defined as:

$$\text{sech}(x) = \frac{2}{e^x + e^{-x}}$$

Where $e$ is the base of the natural logarithm (approximately 2.718).

Syntax

=SECH(number)

Parameters

• number (required): The number for which you want to calculate the hyperbolic secant.

Key Points

1. Hyperbolic Function: The SECH function deals with hyperbolic trigonometry, often used in engineering, physics, and mathematical modeling.
2. Input Domain: The function accepts all real numbers (positive, negative, or zero).
3. Output Range: The result is always between $0$ and $1$.

Examples

1. Calculate the hyperbolic secant of 0:

   =SECH(0)
   

   Result: 1

2. Calculate the hyperbolic secant of 1:

   =SECH(1)
   

   Result: 0.648054

3. Calculate the hyperbolic secant of -1:

   =SECH(-1)
   

   Result: 0.648054

4. Calculate the hyperbolic secant for a value in cell A1:

   =SECH(A1)
   

Errors

• #VALUE!: Occurs if the input is non-numeric or invalid.

Related Functions

• COSH: Calculates the hyperbolic cosine.
• SINH: Calculates the hyperbolic sine.
• TANH: Calculates the hyperbolic tangent.
• CSCH: Calculates the hyperbolic cosecant.
• COTH: Calculates the hyperbolic cotangent.

The SECH function is particularly useful in hyperbolic trigonometry, mathematical modeling, and physics for solving equations involving hyperbolic functions.