mech-math 0.3.4

math/csc
===============================================================================

%% Cosecant of argument in radians

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

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

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

Computes the cosecant 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, csc returns complex results. |

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

| Argument | Kind                     | Description                           |
|----------|--------------------------|---------------------------------------|
| `Y`      | matches input            | Cosecant of the input values. If `X` is real, `Y` is real except where `X` is a multiple of π (where csc 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 cosecant of a number 

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

(b) Find the cosecant for a vector of numbers

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

(c) Find the cosecant for a matrix of numbers

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

(d) Find the cosecant for a matrix of degrees

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

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

The cosecant function is the reciprocal of the sine function:

$$ csc(x) = \frac{1}{sin(x)}

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

$$ csc(x) = \frac{\text{hypotenuse}}{\text{opposite}}

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

$$ csc(x) = \frac{2i}{e^{ix} - e^{-ix}}

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