1. What is Cosh Function?

The cosh (hyperbolic cosine) function is a hyperbolic function that's analogous to the standard cosine function but for a hyperbola rather than a circle. 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 the exponential function and its reciprocal at the given point.

3. Applications of Cosh Function

Details: The cosh function appears in solutions to differential equations, engineering (catenary curves), physics (special relativity), and probability theory.

4. Using the Calculator

Tips: Enter any real number (positive or negative) in radians. The calculator will compute the hyperbolic cosine of the input value.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between cos and cosh?
A: cos is for circular functions (relates to angles in a circle), while cosh is for hyperbolic functions (relates to hyperbolas).

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

Q3: Is cosh(x) the same as cos(ix)?
A: Yes, according to Euler's formula: cosh(x) = cos(ix), where i is the imaginary unit.

Q4: How is this calculated on a Casio calculator?
A: On most Casio calculators, press the "hyp" button followed by "cos" to access the cosh function.

Q5: What are some important identities for cosh?
A: Key identities include: cosh(-x) = cosh(x) (even function), and cosh²x - sinh²x = 1.