✨ 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.
| A | B | C | D | |
|---|---|---|---|---|
| 1 | Year | Projected Growth (%) | Formula | Result |
| 2 | 2020 | 7 | =TANH(B2) | 0.631 |
| 3 | 2021 | 5 | =TANH(B3) | 0.462 |
| 4 | 2022 | 8 | =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.
| A | B | C | D | |
|---|---|---|---|---|
| 1 | Feedback ID | Score | Formula | Result |
| 2 | F001 | 0.9 | =TANH(B2) | 0.716 |
| 3 | F002 | -0.6 | =TANH(B3) | -0.537 |
| 4 | F003 | 0.4 | =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.
| A | B | C | D | |
|---|---|---|---|---|
| 1 | Value | Function Expression | Formula | Result |
| 2 | 0.5 | tanh(x) | =TANH(A2) | 0.462 |
| 3 | -0.75 | tanh(x) | =TANH(A3) | -0.635 |
| 4 | 1.2 | tanh(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.
| A | B | C | D | |
|---|---|---|---|---|
| 1 | Angle (radians) | Normalized Value | Formula | Result |
| 2 | 0.3 | tanh(angle) | =TANH(A2) | 0.291 |
| 3 | 1 | tanh(angle) | =TANH(A3) | 0.761 |
| 4 | -1.5 | tanh(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.
| A | B | C | D | |
|---|---|---|---|---|
| 1 | Input Value | Transformed Value | Formula | Result |
| 2 | 10 | tanh(value) | =TANH(A2) | 1.0 |
| 3 | -10 | tanh(value) | =TANH(A3) | -1.0 |
| 4 | 0 | tanh(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
- Ensure Your Data Is Suitable: Before using the TANH function, ensure your data ranges between -1 and 1 for more meaningful results.
- 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.
- Pair with other Functions: Combine TANH with other Excel functions for more advanced data manipulation.