1. What is the Tanh Function?

The tanh (hyperbolic tangent) function is a hyperbolic analog of the tan function in trigonometry. It's defined as the ratio of the hyperbolic sine to the hyperbolic cosine.

2. How Does the Calculator Work?

The calculator uses the tanh formula:

Where:

• \( \sinh x \) — Hyperbolic sine function
• \( \cosh x \) — Hyperbolic cosine function
• \( x \) — Input value in radians

Explanation: The tanh function takes any real number as input and returns a value between -1 and 1.

3. Applications of Tanh Function

Details: The tanh function is widely used in physics, engineering, and machine learning (as an activation function in neural networks). It's particularly useful for modeling saturation effects.

4. Using the Calculator

Tips: Enter any real number (in radians) to calculate its hyperbolic tangent. The result will be a dimensionless value between -1 and 1.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between tan and tanh?
A: Tan is the circular tangent function (periodic), while tanh is the hyperbolic tangent function (not periodic, approaches ±1 as x → ±∞).

Q2: What are the key properties of tanh?
A: tanh(0) = 0, tanh(-x) = -tanh(x), range is (-1,1), derivative is 1-tanh²(x).

Q3: How is tanh related to exponential functions?
A: tanh x = (eˣ - e⁻ˣ)/(eˣ + e⁻ˣ).

Q4: Why is tanh used in neural networks?
A: Its S-shaped curve and (-1,1) range help with learning patterns while preventing extreme outputs.

Q5: What's the inverse of tanh?
A: The inverse is called artanh or tanh⁻¹, defined for inputs between -1 and 1.