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3 | # Function tanh
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4 |
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5 | Calculate the hyperbolic tangent of a value,
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6 | defined as `tanh(x) = (exp(2 * x) - 1) / (exp(2 * x) + 1)`.
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7 |
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8 | For matrices, the function is evaluated element wise.
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9 |
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10 |
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11 | ## Syntax
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12 |
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13 | ```js
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14 | math.tanh(x)
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15 | ```
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16 |
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17 | ### Parameters
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18 |
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19 | Parameter | Type | Description
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20 | --------- | ---- | -----------
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21 | `x` | number | BigNumber | Complex | Unit | Array | Matrix | Function input
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22 |
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23 | ### Returns
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24 |
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25 | Type | Description
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26 | ---- | -----------
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27 | number | BigNumber | Complex | Array | Matrix | Hyperbolic tangent of x
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28 |
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29 |
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30 | ## Examples
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31 |
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32 | ```js
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33 | // tanh(x) = sinh(x) / cosh(x) = 1 / coth(x)
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34 | math.tanh(0.5) // returns 0.46211715726000974
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35 | math.sinh(0.5) / math.cosh(0.5) // returns 0.46211715726000974
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36 | 1 / math.coth(0.5) // returns 0.46211715726000974
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37 | ```
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38 |
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39 |
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40 | ## See also
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41 |
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42 | [sinh](sinh.md),
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43 | [cosh](cosh.md),
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44 | [coth](coth.md)
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