Hyperbolic Functions

Overview

Engineering reference data for Hyperbolic Functions in mathematics.

Key Formulas

Quadratic Formula

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Roots of ax² + bx + c = 0.

Pythagorean Theorem

$c^2 = a^2 + b^2$

Right triangle relationship.

Circle Area

$A = \pi r^2$

Area of a circle.

Logarithm

$\log_b(x) = \frac{\ln(x)}{\ln(b)}$

Change of base formula.

Variables

Values for Hyperbolic Functions

The following table provides computed values for the primary hyperbolic functions and their related exponentials.

Inverse Hyperbolic Functions

The inverse functions for the primary hyperbolic functions are defined as follows:

$$\sinh^{-1}(x) = \log_e\left(x + \sqrt{x^2 + 1}\right)$$ $$\cosh^{-1}(x) = \log_e\left(x \pm \sqrt{x^2 - 1}\right), \quad x \geq 1$$ $$\tanh^{-1}(x) = \frac{1}{2} \log_e\left(\frac{1 + x}{1 - x}\right), \quad |x| < 1$$

Interactive Charts

References

• Original Source