ACOTH function

The ACOTH function in Excel returns the inverse hyperbolic cotangent of a number. It calculates the angle whose hyperbolic cotangent is the given number.

Syntax

=ACOTH(number)

Parameters

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

How It Works

The ACOTH function calculates the inverse hyperbolic cotangent of a number. The result is returned in radians, and it will be in the range from 0 to π (0 to 180 degrees).

Examples

Example 1: Using ACOTH with a Number Greater Than 1

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

=ACOTH(A1)

will return 0.4636 (which is the inverse hyperbolic cotangent 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(ACOTH(A1))

If A1 is 2, this will return 26.57 degrees.

Example 3: Invalid Input (Number Between -1 and 1)

If the value in A2 is 0.5, the formula:

=ACOTH(A2)

will return an error #NUM!, as the inverse hyperbolic cotangent is only defined for numbers greater than 1 or less than -1.

Key Points

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

Use Cases

• Mathematics and Engineering: Useful when solving equations involving hyperbolic cotangent functions or in problems requiring inverse hyperbolic calculations.
• Physics: Can be applied in certain wave functions, oscillations, or other areas where hyperbolic cotangent properties are involved.