1. What is Hyperbolic Tangent?

The hyperbolic tangent (tanh) is a hyperbolic function that is the ratio of hyperbolic sine to hyperbolic cosine. It's analogous to the ordinary tangent function but for a hyperbola rather than a circle.

2. How Does the Calculator Work?

The calculator uses the hyperbolic tangent formula:

Where:

• \( x \) — Input value in radians
• \( e \) — Euler's number (~2.71828)
• \( \sinh(x) \) — Hyperbolic sine function
• \( \cosh(x) \) — Hyperbolic cosine function

Explanation: The function approaches 1 as x approaches infinity and -1 as x approaches negative infinity, making it useful as an activation function in neural networks.

3. Applications of Hyperbolic Tangent

Details: The tanh function is widely used in physics, engineering, and machine learning. In neural networks, it serves as an activation function that maps inputs to values between -1 and 1.

4. Using the Calculator

Tips: Enter any real number as the argument. The calculator will compute both the built-in tanh function and the exponential formula for verification.

5. Frequently Asked Questions (FAQ)

Q1: What's the range of tanh function?
A: The tanh function outputs values between -1 and 1 for all real inputs.

Q2: How does tanh differ from regular tangent?
A: While both are ratio functions, tanh relates to hyperbolas and is bounded between -1 and 1, whereas regular tangent relates to circles and is unbounded.

Q3: Why is tanh used in neural networks?
A: Its S-shaped curve and range (-1 to 1) make it useful for normalizing outputs and providing non-linearity while maintaining strong gradients.

Q4: What's the derivative of tanh?
A: The derivative is \( 1 - \tanh^2(x) \), which is computationally convenient for backpropagation in neural networks.

Q5: Are there inverse hyperbolic tangent functions?
A: Yes, the inverse is called artanh or tanh⁻¹, defined for values between -1 and 1.