1. What is Cosh Function?

The cosh (hyperbolic cosine) function is a hyperbolic function that's analogous to the standard cosine function but for hyperbolas instead of circles. It's defined using exponential functions.

2. How Does the Calculator Work?

The calculator uses the cosh formula:

Where:

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

Explanation: The function calculates the average of eˣ and e⁻ˣ, which gives the hyperbolic cosine of x.

3. Applications of Cosh Function

Details: The cosh function appears in solutions to differential equations, engineering (especially suspension bridge calculations), special relativity, and heat transfer problems.

4. Using the Calculator

Tips: Enter any real number (positive or negative) in radians. The result is dimensionless.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between cos and cosh?
A: cos is for circular functions (periodic), while cosh is for hyperbolic functions (exponential growth).

Q2: What is the range of cosh function?
A: The range is [1, ∞). The minimum value is 1 at x=0.

Q3: Is cosh(x) always positive?
A: Yes, cosh(x) is always positive for all real x.

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

Q5: How is cosh related to catenary curves?
A: A hanging chain forms a catenary curve described by y = a·cosh(x/a).