# 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

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

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

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