Add TAN function description

docs/src/functions/math-and-trigonometry.md

@@ -90,6 +90,6 @@ You can track the progress in this [GitHub issue](https://github.com/ironcalc/Ir
 | SUMX2MY2        | <Badge type="info" text="Not implemented yet" /> | –             |
 | SUMX2PY2        | <Badge type="info" text="Not implemented yet" /> | –             |
 | SUMXMY2         | <Badge type="info" text="Not implemented yet" /> | –             |
-| TAN             | <Badge type="tip" text="Available" />          | –             |
+| TAN             | <Badge type="tip" text="Available" />          | [TAN](math_and_trigonometry/tan) |
 | TANH            | <Badge type="tip" text="Available" />          | –             |
 | TRUNC           | <Badge type="info" text="Not implemented yet" /> | –             |

docs/src/functions/math_and_trigonometry/tan.md

@@ -3,9 +3,42 @@ layout: doc
 outline: deep
 lang: en-US
 ---
-
-# TAN
-
+# TAN function
 ::: warning
-🚧 This function is implemented but currently lacks detailed documentation. For guidance, you may refer to the equivalent functionality in [Microsoft Excel documentation](https://support.microsoft.com/en-us/office/excel-functions-by-category-5f91f4e9-7b42-46d2-9bd1-63f26a86c0eb).
+**Note:** This draft page is under construction 🚧
 :::
+## Overview
+TAN is a function of the Math and Trigonometry category that calculates the trigonometric tangent of an angle, returning a value in the range (-$\infty$, +$\infty$).
+## Usage
+### Syntax
+**TAN(<span title="Number" style="color:#1E88E5">angle</span>) => <span title="Number" style="color:#1E88E5">tan</span>**
+### Argument descriptions
+* *angle* ([number](/features/value-types#numbers), required). The angle whose tangent is to be calculated, expressed in radians. To convert between degrees and radians, use the relation below. Alternatively, use the [DEGREES](/functions/math_and_trigonometry/degrees) or [RADIANS](/functions/math_and_trigonometry/radians) functions.
+$$
+1~\:~\text{degree} = \dfrac{\pi}{180} = 0.01745329252~\text{radians}
+$$
+
+### Additional guidance
+None.
+### Returned value
+TAN returns a unitless [number](/features/value-types/#numbers) that is the trigonometric tangent of the specified angle.
+### Error conditions
+* In common with many other IronCalc functions, TAN propagates errors that are found in its argument.
+* If no argument, or more than one argument, is supplied, then TAN returns the [`#ERROR!`](/features/error-types.md#error) error.
+* If the value of the *angle* argument is not (or cannot be converted to) a [number](/features/value-types#numbers), then TAN returns the [`#VALUE!`](/features/error-types.md#value) error.
+* For some argument values, TAN may return a [`#DIV/0!`](/features/error-types.md#div-0) error.
+<!--@include: ../markdown-snippets/error-type-details.txt-->
+## Details
+* The TAN function utilizes the *tan()* method provided by the [Rust Standard Library](https://doc.rust-lang.org/std/).
+* The figure below illustrates the output of the TAN function for angles $x$ in the range -2$π$ to +2$π$.
+<center><img src="/functions/images/tangent-curve.png" width="350" alt="Graph showing tan(x) for x between -2π and +2π."></center>
+
+* Theoretically, $\text{tan}(x)$ is undefined for any critical $x$ that satisfies $x = \frac{\pi}{2} + k\pi$ (where $k$ is any integer). However, an exact representation of the mathmatical constant $\pi$ requires infinite precision, which cannot be achieved with the floating-point representation available. Hence, TAN will return very large or very small values close to critical $x$ values.
+## Examples
+[See some examples in IronCalc](https://app.ironcalc.com/?example=tan).
+
+## Links
+* For more information about trigonometric tangent, visit Wikipedia's [Trigonometric functions](https://en.wikipedia.org/wiki/Trigonometric_functions) page.
+* See also IronCalc's [ATAN](/functions/math_and_trigonometry/atan), [COS](/functions/math_and_trigonometry/cos) and [SIN](/functions/math_and_trigonometry/sin) functions.
+* Visit Microsoft Excel's [TAN function](https://support.microsoft.com/en-gb/office/tan-function-08851a40-179f-4052-b789-d7f699447401) page.
+* Both [Google Sheets](https://support.google.com/docs/answer/3093586) and [LibreOffice Calc](https://wiki.documentfoundation.org/Documentation/Calc_Functions/TAN) provide versions of the TAN function.