mech-math 0.3.3

Math library for the Mech language
Documentation 
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math/cot
===============================================================================

%% Cotangent of argument in radians

1. Usage
-------------------------------------------------------------------------------

```mech:disabled
Y := math/cot(X)
```

2. Description
-------------------------------------------------------------------------------

Computes the cotangent of each element of `X`. The input `X` is interpreted in radians, not degrees. The result `Y` has the same shape as the input `X`.

3. Input
-------------------------------------------------------------------------------

| Argument | Kind                     | Description                           |
|----------|--------------------------|---------------------------------------|
| `X`      | `float`, `[float]`       | Input angle(s) specified in radians. Can be real or complex. If `X` is complex, cot returns complex results. |

4. Output
-------------------------------------------------------------------------------

| Argument | Kind                     | Description                           |
|----------|--------------------------|---------------------------------------|
| `Y`      | matches input            | Cotangent of the input values. If `X` is real, `Y` is real except where `X` is a multiple of π (where cot is undefined). If `X` is complex, `Y` may have both real and imaginary parts. The shape of `Y` matches the shape of `X`. |

5. Examples  
-------------------------------------------------------------------------------

(a) Find the cotangent of a number 

```mech:ex1
y := math/cot(1.0)
```

(b) Find the cotangent for a vector of numbers

```mech:ex2
x := [0.5, 1.0, 1.5]
y := math/cot(x)
```

(c) Find the cotangent for a matrix of numbers

```mech:ex3
x := [0.5, 1.0; 1.5, 2.0]
y := math/cot(x)
```

(d) Find the cotangent for a matrix of degrees

```mech:ex4
x := [30, 45; 60, 90]
y := math/cot(x * 3.14 / 180)
```

6. Details
-------------------------------------------------------------------------------

The cotangent function is the reciprocal of the tangent function:

$$ cot(x) = \frac{1}{tan(x)}

In a right triangle, the cotangent of an angle $$x$$ is defined as the ratio of the length of the adjacent side to the opposite side:

$$ cot(x) = \frac{\text{adjacent}}{\text{opposite}}

For complex numbers, the cotangent can be expressed in terms of exponentials:

$$ cot(x) = i \cdot \frac{e^{ix} + e^{-ix}}{e^{ix} - e^{-ix}}

This definition extends the cotangent function to work beyond real numbers, allowing it to handle complex inputs.