Inverse Hyperbolic Function Evaluation
Inverse Hyperbolic Function Evaluation
\[\begin{aligned}
\sinh^{-1}(x) &= \ln(x+\sqrt{x^2+1}) \\
\cosh^{-1}(x) &= \ln(x+\sqrt{x^2-1}) \\
\tanh^{-1}(x) &= \frac{1}{2}\ln\left(\frac{1+x}{1-x}\right)
\end{aligned}\]
Variables
asinh = inverse hyperbolic sine value
acosh = inverse hyperbolic cosine value
atanh = inverse hyperbolic tangent value
x = independent variable
Description
What is this formula?
These formulas calculate inverse hyperbolic functions using logarithmic expressions. They determine the hyperbolic angle corresponding to a given value.
When to use it
Use these formulas when solving equations involving hyperbolic functions or modeling logarithmic-hyperbolic relationships.
Example
For:
x=2
asinh=ln(2+sqrt(5))
asinh≈1.444
Applications
Advanced calculus
Differential equations
Electrical engineering
Relativity physics
Signal analysis
Mathematical modeling
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