Hyperbolic Trig Functions

#Math
Video Definition
Desmos Interactive

Definitions

• $\sinh x = \frac{e^x - e^{-x}}{2}$
• $\cosh x = \frac{e^x + e^{-x}}{2}$
• $\tanh x = \frac{\sinh x}{\cosh x}$
• $\text{csch } x = \frac{1}{\sinh x}$
• $\text{sech} x = \frac{1}{\cosh x}$
• $\text{coth } x = \frac{\cosh x}{\sinh x}$

Identities

• $\sinh (-x) = -\sinh x$
• $\cosh (-x) = \cosh x$
• $\cosh^2 x - \sinh^2 x = 1$
• $1 - \tanh^2 x = \text{sech}^2 x$
• $\sinh(x + y) = \sinh x \cosh y + \cosh x \sinh y$
• $\cosh (x + y) = \cosh x \cosh y + \sinh x \sinh y$