# Function tanh Calculate the hyperbolic tangent of a value, defined as `tanh(x) = (exp(2 * x) - 1) / (exp(2 * x) + 1)`. For matrices, the function is evaluated element wise. ## Syntax ```js math.tanh(x) ``` ### Parameters Parameter | Type | Description --------- | ---- | ----------- `x` | number | BigNumber | Complex | Unit | Array | Matrix | Function input ### Returns Type | Description ---- | ----------- number | BigNumber | Complex | Array | Matrix | Hyperbolic tangent of x ### Throws Type | Description ---- | ----------- ## Examples ```js // tanh(x) = sinh(x) / cosh(x) = 1 / coth(x) math.tanh(0.5) // returns 0.46211715726000974 math.sinh(0.5) / math.cosh(0.5) // returns 0.46211715726000974 1 / math.coth(0.5) // returns 0.46211715726000974 ``` ## See also [sinh](sinh.md), [cosh](cosh.md), [coth](coth.md)