Sinh Function Calculator

Hyperbolic Sine Function:

\[ \sinh(x) = \frac{e^x - e^{-x}}{2} \]

sinh(x):

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1. What is the Sinh Function?

The sinh (hyperbolic sine) function is one of the basic hyperbolic functions. It's defined using exponential functions and is analogous to the ordinary sine function but for a hyperbola rather than a circle.

2. How Does the Calculator Work?

The calculator uses the standard definition of sinh:

\[ \sinh(x) = \frac{e^x - e^{-x}}{2} \]

Where:

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

Explanation: The function calculates the difference between exponential growth and decay, divided by two.

3. Applications of Sinh Function

Details: The sinh function appears in solutions to differential equations, calculations of catenary curves, special relativity, and electrical engineering.

4. Using the Calculator

Tips: Enter any real number value in radians. The calculator will compute the hyperbolic sine of the input value.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between sin and sinh?
A: sin is a circular trigonometric function, while sinh is a hyperbolic function. They have different properties and applications.

Q2: What is the range of sinh(x)?
A: The range of sinh(x) is all real numbers (-∞, ∞).

Q3: Is sinh(x) the same as (e^x)/2?
A: Only for large positive x where e^(-x) becomes negligible. For other values, both terms are significant.

Q4: What is the derivative of sinh(x)?
A: The derivative is cosh(x) (hyperbolic cosine function).

Q5: Can I use degrees instead of radians?
A: No, hyperbolic functions always use radians as their input unit.