\[\begin{aligned}
\sinh(x) &= \frac{e^x-e^{-x}}{2} \\
\cosh(x) &= \frac{e^x+e^{-x}}{2} \\
\tanh(x) &= \frac{e^x-e^{-x}}{e^x+e^{-x}}
\end{aligned}\]
Variables
sinhhyperbolic sine value
coshhyperbolic cosine value
tanhhyperbolic tangent value
xindependent variable
Description
What is this formula?
These formulas calculate the main hyperbolic functions using exponential expressions. Hyperbolic functions are analogous to trigonometric functions but are based on hyperbolas instead of circles.
When to use it
Use these formulas when solving differential equations, modeling catenary curves or analyzing hyperbolic relationships.
Example
For:
x=1
sinh=((℮^1)-(℮^(-1)))/2≈1.175
cosh=((℮^1)+(℮^(-1)))/2≈1.543
tanh=((℮^1)-(℮^(-1)))/((℮^1)+(℮^(-1)))≈0.762
Applications
Differential equations
Relativity physics
Electrical engineering
Signal processing
Catenary analysis
Mathematical modeling