cosh
Represents the hyperbolic cosine function, a fundamental mathematical operation used in hyperbolic geometry and engineering calculations.
Overview
Essential in advanced mathematics and physics applications where hyperbolic functions play a key role.
- Commonly used in analyzing physical phenomena like catenary curves and electrical signals
- Appears frequently in differential equations, especially those modeling wave propagation
- Important in special relativity and electromagnetic theory
- Often paired with sinh and tanh in mathematical expressions
- Particularly useful in solving problems involving exponential growth and decay
Examples
Definition of hyperbolic cosine in terms of exponentials.
\cosh x = \frac{e^x + e^{-x}}{2}Solution to a hyperbolic differential equation.
y(x) = A\cosh(\lambda x) + B\sinh(\lambda x)Identity relating hyperbolic cosine to regular cosine.
\cosh(ix) = \cos(x)