Jak używać funkcji TANH w Excelu

Introduction to the TANH Function

The TANH function, known as the hyperbolic tangent, is a mathematical function available in both Microsoft Excel and Google Sheets. It is especially useful in various fields such as engineering, mathematics, finance, and data analysis. It returns the hyperbolic tangent of a given number.

Syntax and Examples

The syntax for the TANH function is straightforward:

=TANH(number)

Here, number refers to the value for which the hyperbolic tangent is calculated.

Examples of usage in a spreadsheet include:

=TANH(0) – Returns 0, as the hyperbolic tangent of zero is zero.
=TANH(1) – Returns approximately 0.7616, which is the hyperbolic tangent of one.

Applications of the Function in Practical Scenarios

Population Growth Analysis

Consider a study on the population growth of a certain animal species, which you wish to model using a hyperbolic function. Assume that population growth over time (t) can be described by:

Population(t) = maximum_population * TANH(0.03 * t)

For instance, if the maximum forecasted population is 1000 individuals, using Excel or Google Sheets, you can compute the population after 10, 20, and 30 days:

Time (t)	Formula	Result
10 days	`=1000 * TANH(0.03 * 10)`	258.18
20 days	`=1000 * TANH(0.03 * 20)`	462.11
30 days	`=1000 * TANH(0.03 * 30)`	576.68

Application in Finance to Assess Investment Risk

Suppose you are a financial analyst looking to evaluate investment risk that changes over time and you want to use the TANH function to smooth the risk values, which tend to an asymptotic level. This scenario can be modeled as follows:

Risk(t) = max_risk * TANH(scaling * t)

For simplicity, let”s assume max_risk as 100%, and scaling as 0.05. We can then explore how the risk changes over time (t=0 to t=50) in steps of 10:

Time (t)	Formula	Result
0 days	`=100 * TANH(0.05 * 0)`	0%
10 days	`=100 * TANH(0.05 * 10)`	48.49%
20 days	`=100 * TANH(0.05 * 20)`	76.10%
30 days	`=100 * TANH(0.05 * 30)`	87.97%
40 days	`=100 * TANH(0.05 * 40)`	93.59%
50 days	`=100 * TANH(0.05 * 50)`	96.42%