The COTH function in Google Sheets is used to compute the hyperbolic cotangent of a given real number. This mathematical function is essential in various fields such as engineering, physics, and advanced mathematics, particularly when dealing with equations that involve hyperbolic functions. Understanding how to use COTH effectively can provide insights into complex calculations involving hyperbolic trigonometry.

Syntax

COTH(value)

• value: This is the real number for which you want to find the hyperbolic cotangent.

Example #1

COTH(1)

This function will return the hyperbolic cotangent of 1, yielding a value of approximately 1.313, which can be useful in trigonometric applications.

Example #2

COTH(0.5)

Here, the function calculates the hyperbolic cotangent of 0.5, resulting in about 1.543. This result can aid in various scientific calculations involving hyperbolic functions.

Example #3

COTH(-2)

In this case, the function returns the hyperbolic cotangent of -2, approximately -0.450. This illustrates how COTH can also handle negative inputs effectively.

Error handling

• DIV/0! This error occurs when the input value is exactly zero, as the hyperbolic cotangent is undefined for this case.
• NUM! This error appears if the function receives a non-numeric argument, indicating that the input must be a valid real number.

Conclusion

In summary, the COTH function is a powerful tool in Google Sheets for calculating the hyperbolic cotangent of real numbers. It plays a critical role in various mathematical and scientific applications. By understanding the syntax and handling potential errors, users can effectively incorporate this function into their spreadsheet calculations.