acosh - Linux

Overview

acosh calculates the inverse hyperbolic cosine of a given numeric argument. It is commonly used in mathematical applications involving complex numbers, trigonometry, and hyperbolic functions.

Syntax

acosh NUMBER

Where:

• NUMBER: The numeric value for which the inverse hyperbolic cosine is calculated.

Options/Flags

None.

Examples

Basic Usage

Calculate the inverse hyperbolic cosine of 2:

$ acosh 2
1.3169578969248166

Real-World Application

Find the time taken for a particle to reach a certain distance in a hyperbolic trajectory:

# Distance in hyperbolic units
d=4.5

# Velocity in hyperbolic units
v=1.2

# Time taken in hyperbolic units
t=acosh(d/v)

echo "Time taken: $t hyperbolic units"

Common Issues

• Invalid Input: A non-numeric input or a negative value will result in an error.

Integration

acosh can be combined with other commands to perform complex calculations. For instance, it can be used with bc to evaluate complex expressions:

$ echo "scale=20; acosh(2)" | bc
1.3169578969248166

Related Commands

• cosh: Calculate the hyperbolic cosine.
• sinh: Calculate the hyperbolic sine.
• tanh: Calculate the hyperbolic tangent.