# TANH Function in Excel

## ✨ Part 1: Introduce

### 📌 Definition

The TANH function in Excel returns the hyperbolic tangent of a number.

### 📌 Purpose

This function is particularly beneficial when normalizing data. In mathematics and various fields, the hyperbolic tangent of a number can be a useful metric.

### 📌 Syntax & Arguments

`=TANH(number)`

Where the argument is:

• `number` – This is a mandatory argument, which can be a real number or a reference to a cell containing a number.

### 📌 Return value

The function will return the hyperbolic tangent of the specified number.

### 📌 Remarks

The result will always be between -1 and 1.

## ✨ Part 2: Examples

### 📌 Example 1: Sales Growth Analysis

Purpose: Determine the relation between projected and actual sales growth.

ABCD
1YearProjected Growth (%)FormulaResult
220207=TANH(B2)0.631
320215=TANH(B3)0.462
420228=TANH(B4)0.712

Explanation: The TANH of the projected growth percentage can help businesses understand how growth is expected to stabilize over time.

### 📌 Example 2: Customer Feedback Analysis

Purpose: Measure the intensity of customer feedback scores.

ABCD
1Feedback IDScoreFormulaResult
2F0010.9=TANH(B2)0.716
3F002-0.6=TANH(B3)-0.537
4F0030.4=TANH(B4)0.379

Explanation: Positive feedback scores nearer to 1 indicate strong positive feedback, whereas scores closer to -1 show strong negative feedback.

### 📌 Example 3: Evaluating Mathematical Functions

Purpose: Explore the behavior of the hyperbolic tangent function for different mathematical values.

ABCD
1ValueFunction ExpressionFormulaResult
20.5tanh(x)=TANH(A2)0.462
3-0.75tanh(x)=TANH(A3)-0.635
41.2tanh(x)=TANH(A4)0.833

Explanation: This table helps visualize how the hyperbolic tangent function behaves for various mathematical inputs. The function compresses the input range between -1 and 1.

### 📌 Example 4: Normalizing Data in Trigonometry

Purpose: Normalize angles in radians for further trigonometric analyses.

ABCD
20.3tanh(angle)=TANH(A2)0.291
31tanh(angle)=TANH(A3)0.761
4-1.5tanh(angle)=TANH(A4)-0.905

Explanation: When working with angles in trigonometry, especially in radians, the TANH function can help normalize values, making them suitable for specific calculations or graphical representations.

### 📌 Example 5: Transforming Linear Data

Purpose: Utilize the TANH function to compress linearly increasing values into a -1 to 1 range.

ABCD
1Input ValueTransformed ValueFormulaResult
210tanh(value)=TANH(A2)1.0
3-10tanh(value)=TANH(A3)-1.0
40tanh(value)=TANH(A4)0.0

Explanation: This example showcases the ability of the TANH function to transform a broad range of linear data into the interval between -1 and 1. This property is beneficial for normalizing data or handling significant input-value variations.

## ✨ Part 3: Tips and Tricks

1. Ensure Your Data Is Suitable: Before using the TANH function, ensure your data ranges between -1 and 1 for more meaningful results.
2. Use With Neural Networks: TANH can be a crucial activation function in particular neural network layers, as it scales values to a -1 to 1 range.
3. Pair with other Functions: Combine TANH with other Excel functions for more advanced data manipulation.