Hyperbolic Trig Functions

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

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