> ## Documentation Index
> Fetch the complete documentation index at: https://numpyts.dev/llms.txt
> Use this file to discover all available pages before exploring further.

# Hyperbolic

> Element-wise hyperbolic functions and their inverses.

All hyperbolic functions operate element-wise.

### sinh

Compute the hyperbolic sine, element-wise.

```typescript theme={null}
function sinh(x: ArrayLike): NDArray
```

| Name | Type        | Default | Description  |
| ---- | ----------- | ------- | ------------ |
| `x`  | `ArrayLike` | -       | Input array. |

**Returns:** `NDArray` -- Element-wise `sinh(x) = (exp(x) - exp(-x)) / 2`.

<CodeGroup>
  ```typescript Full Library theme={null}
  import * as np from 'numpy-ts';

  const a = np.sinh(np.array([0, 1, -1]));
  // array([0, 1.1752..., -1.1752...])
  ```

  ```typescript Core theme={null}
  import { sinh, array } from 'numpy-ts/core';

  const a = sinh(array([0, 1, -1]));
  ```
</CodeGroup>

***

### cosh

Compute the hyperbolic cosine, element-wise.

```typescript theme={null}
function cosh(x: ArrayLike): NDArray
```

| Name | Type        | Default | Description  |
| ---- | ----------- | ------- | ------------ |
| `x`  | `ArrayLike` | -       | Input array. |

**Returns:** `NDArray` -- Element-wise `cosh(x) = (exp(x) + exp(-x)) / 2`.

<CodeGroup>
  ```typescript Full Library theme={null}
  import * as np from 'numpy-ts';

  const a = np.cosh(np.array([0, 1, -1]));
  // array([1, 1.5431..., 1.5431...])
  ```

  ```typescript Core theme={null}
  import { cosh, array } from 'numpy-ts/core';

  const a = cosh(array([0, 1, -1]));
  ```
</CodeGroup>

***

### tanh

Compute the hyperbolic tangent, element-wise.

```typescript theme={null}
function tanh(x: ArrayLike): NDArray
```

| Name | Type        | Default | Description  |
| ---- | ----------- | ------- | ------------ |
| `x`  | `ArrayLike` | -       | Input array. |

**Returns:** `NDArray` -- Element-wise `tanh(x) = sinh(x) / cosh(x)`.

<CodeGroup>
  ```typescript Full Library theme={null}
  import * as np from 'numpy-ts';

  const a = np.tanh(np.array([0, 1, -1, 100]));
  // array([0, 0.7616..., -0.7616..., 1])
  ```

  ```typescript Core theme={null}
  import { tanh, array } from 'numpy-ts/core';

  const a = tanh(array([0, 1, -1]));
  ```
</CodeGroup>

***

### arcsinh

Compute the inverse hyperbolic sine, element-wise. Also available as the alias `asinh`.

```typescript theme={null}
function arcsinh(x: ArrayLike): NDArray
```

| Name | Type        | Default | Description  |
| ---- | ----------- | ------- | ------------ |
| `x`  | `ArrayLike` | -       | Input array. |

**Returns:** `NDArray` -- Element-wise `arcsinh(x) = ln(x + sqrt(x**2 + 1))`.

<CodeGroup>
  ```typescript Full Library theme={null}
  import * as np from 'numpy-ts';

  const a = np.arcsinh(np.array([0, 1, -1]));
  // array([0, 0.8814..., -0.8814...])

  // Alias
  const b = np.asinh(np.array([0, 1]));
  ```

  ```typescript Core theme={null}
  import { arcsinh, array } from 'numpy-ts/core';
  // or: import { asinh } from 'numpy-ts/core';

  const a = arcsinh(array([0, 1, -1]));
  ```
</CodeGroup>

***

### arccosh

Compute the inverse hyperbolic cosine, element-wise. Also available as the alias `acosh`.

```typescript theme={null}
function arccosh(x: ArrayLike): NDArray
```

| Name | Type        | Default | Description                             |
| ---- | ----------- | ------- | --------------------------------------- |
| `x`  | `ArrayLike` | -       | Input array. All values must be `>= 1`. |

**Returns:** `NDArray` -- Element-wise `arccosh(x) = ln(x + sqrt(x**2 - 1))`.

<CodeGroup>
  ```typescript Full Library theme={null}
  import * as np from 'numpy-ts';

  const a = np.arccosh(np.array([1, 2, 10]));
  // array([0, 1.3170..., 2.9932...])

  // Alias
  const b = np.acosh(np.array([1, 2]));
  ```

  ```typescript Core theme={null}
  import { arccosh, array } from 'numpy-ts/core';
  // or: import { acosh } from 'numpy-ts/core';

  const a = arccosh(array([1, 2, 10]));
  ```
</CodeGroup>

***

### arctanh

Compute the inverse hyperbolic tangent, element-wise. Also available as the alias `atanh`.

```typescript theme={null}
function arctanh(x: ArrayLike): NDArray
```

| Name | Type        | Default | Description                                             |
| ---- | ----------- | ------- | ------------------------------------------------------- |
| `x`  | `ArrayLike` | -       | Input array. All values must be in the range `(-1, 1)`. |

**Returns:** `NDArray` -- Element-wise `arctanh(x) = 0.5 * ln((1+x) / (1-x))`.

<CodeGroup>
  ```typescript Full Library theme={null}
  import * as np from 'numpy-ts';

  const a = np.arctanh(np.array([0, 0.5, -0.5]));
  // array([0, 0.5493..., -0.5493...])

  // Alias
  const b = np.atanh(np.array([0, 0.5]));
  ```

  ```typescript Core theme={null}
  import { arctanh, array } from 'numpy-ts/core';
  // or: import { atanh } from 'numpy-ts/core';

  const a = arctanh(array([0, 0.5, -0.5]));
  ```
</CodeGroup>