# Other trigonometric functions

## Other

### Other functions

#### Reciprocal trigonometric functions

Standard

\(\csc (\theta ):=\dfrac{1}{\sin (\theta )}\)

\(\sec (\theta ):=\dfrac{1}{\cos (\theta )}\)

\(\cot (\theta ):=\dfrac{1}{\tan (\theta )}\)

Hyperbolic

\(csch (\theta ):=\dfrac{1}{\sinh (\theta )}\)

\(sech (\theta ):=\dfrac{1}{\cosh (\theta )}\)

\(coth (\theta ):=\dfrac{1}{\tanh (\theta )}\)

#### Inverse trigonometric functions

Reciprocal standard

\(\csc (arccsc (\theta )):=\theta \)

\(\sec (arcsec (\theta )):=\theta \)

\(\cot (arccot (\theta )):=\theta \)

Reciprocal hyperbolic

\(csch (arccsch (\theta )):=\theta \)

\(sech (arcsech (\theta )):=\theta \)

\(coth (arccoth (\theta )):=\theta \)

## Hyperbolic functions

### Hyperbolic functions

#### Hyperbolic functions

\(\sinh(\theta ):=\sin(i\theta )\)

\(\cosh(\theta ):=\cos(i\theta )\)

\(\tanh(\theta ):=\tan(i\theta )\)

#### Inverse trigonometric functions

\(\sinh (arcsinh (\theta )):=\theta \)

\(\cosh (arccosh (\theta )):=\theta \)

\(\tanh (arctan (\theta )):=\theta \)