ACOSH function

The ACOSH function in Excel returns the inverse hyperbolic cosine (arc hyperbolic cosine) of a number. It is used to find the angle (in radians) whose hyperbolic cosine is a given number.

Syntax

=ACOSH(number)

Parameters

• number: This is a required argument. It is the value for which you want to find the inverse hyperbolic cosine. The number must be greater than or equal to 1. If the number is less than 1, the function will return an error (#NUM!).

How It Works

The ACOSH function calculates the inverse hyperbolic cosine of a number, which is the value whose hyperbolic cosine equals the given number. The result is returned in radians. The inverse hyperbolic cosine function is defined only for values greater than or equal to 1.

Examples

Example 1: Using ACOSH with a Valid Number

If the value in cell A1 is 2, the formula:

=ACOSH(A1)

will return 1.31696 (which is the inverse hyperbolic cosine of 2, in radians).

Example 2: Converting Radians to Degrees

If you want the result in degrees instead of radians, you can use the DEGREES function. For example:

=DEGREES(ACOSH(A1))

If A1 is 2, this will return 75.54 degrees.

Example 3: Invalid Input (Number Less Than 1)

If the value in A2 is 0.5, the formula:

=ACOSH(A2)

will return an error #NUM!, as the inverse hyperbolic cosine is only defined for numbers greater than or equal to 1.

Key Points

• The ACOSH function returns the inverse hyperbolic cosine of a number in radians.
• The number must be greater than or equal to 1; otherwise, the function will return a #NUM! error.
• To convert the result to degrees, use the DEGREES function in combination with ACOSH.

Use Cases

• Mathematics and Engineering: Useful in problems related to hyperbolic functions, such as in mechanical systems, signal processing, or when working with hyperbolic geometry.
• Physics: Can be used in situations involving relativistic physics, as hyperbolic functions often appear in calculations involving velocity or acceleration in certain contexts.