COSH function

The COSH function in Excel returns the hyperbolic cosine of a number. The hyperbolic cosine is similar to the regular cosine, but it is defined using exponential functions.

Syntax

=COSH(number)

Parameters

• number: The number for which you want to find the hyperbolic cosine. This value can be any real number.

Return Value

The function returns the hyperbolic cosine of the given number.

How It Works

The COSH function computes the hyperbolic cosine of a number using the following formula:

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

Where:

• e is the base of the natural logarithm (approximately equal to 2.71828).
• x is the input number.

Example 1: Hyperbolic Cosine of a Number

To calculate the hyperbolic cosine of 1:

=COSH(1)

Result: 1.5431
(The hyperbolic cosine of 1 is approximately 1.5431.)

Example 2: Hyperbolic Cosine of 0

To calculate the hyperbolic cosine of 0:

=COSH(0)

Result: 1
(The hyperbolic cosine of 0 is exactly 1.)

Example 3: Hyperbolic Cosine of a Negative Number

To calculate the hyperbolic cosine of -2:

=COSH(-2)

Result: 3.7622
(The hyperbolic cosine of -2 is approximately 3.7622.)

Important Notes

• The COSH function always returns a positive value or 1 for 0, since the hyperbolic cosine is always greater than or equal to 1 for all real numbers.
• The COSH function is useful in advanced mathematical calculations, particularly in the context of hyperbolic geometry and complex analysis.

Use Cases

• Mathematics and Engineering: Used in various formulas, including those for waveforms, oscillations, and electrical engineering applications.
• Graphing: The COSH function can be graphed to visualize the hyperbolic cosine curve, which looks similar to the regular cosine curve but grows exponentially as the input number increases or decreases.