1. What is Tanh Function?

The hyperbolic tangent (tanh) function is a mathematical function that relates to the standard trigonometric tangent function but for hyperbolic rather than circular geometry. It ranges between -1 and 1.

2. How Does the Calculator Work?

The calculator uses the tanh formula:

Where:

• \( x \) — Input value in radians
• \( e \) — Euler's number (~2.71828)

Explanation: The function calculates the ratio of the difference to the sum of exponential functions of the input value and its negative.

3. Applications of Tanh

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 situations with saturation effects.

4. Using the Calculator

Tips: Enter any real number value in radians. The calculator will return a value between -1 and 1.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between tan and tanh?
A: Tan is for circular trigonometry (relating to circles), while tanh is for hyperbolic trigonometry.

Q2: What are the asymptotes of tanh?
A: Tanh approaches 1 as x approaches infinity and -1 as x approaches negative infinity.

Q3: How is tanh related to sigmoid function?
A: The tanh function is a scaled and shifted version of the sigmoid function (tanh(x) = 2σ(2x) - 1).

Q4: What's the derivative of tanh?
A: The derivative is 1 - tanh²(x), which makes it convenient for backpropagation in neural networks.

Q5: Can tanh be used with degrees?
A: The standard tanh function uses radians, but you can convert degrees to radians first (radians = degrees × π/180).