Trigonometric & Mathematical Constants Table Markdown Table Template

When to Use This Table

Formatting This Table in Markdown

A trigonometric & mathematical constants table table puts a few things in cells that Markdown treats as syntax. These are the ones to watch so it renders correctly on GitHub, GitLab, Obsidian and docs sites.

• Math headers need a math renderer; plain Unicode does not

  Headers such as $\sin(\theta)$ render as math on GitHub, GitLab and Obsidian, but docs generators like MkDocs or Docusaurus need a math plugin, and elsewhere the dollar signs show as literal text. If the table must read correctly everywhere, write sin θ in the header and keep LaTeX for pages you control; see math in tables.

• Pick code spans or math for the values, not both

  A value in a code span, like √3/2, shows exactly as typed in monospace, while $\frac{\sqrt{3}}{2}$ typesets a stacked fraction and makes that row taller. Mixing the two in one column makes the exact values look inconsistent, so choose one style per column.

• Add a column people can paste into code

  Symbols such as √3/2 and π/6 read well, but most languages need a function call such as sqrt(3)/2 or a decimal. A code-ready column, or decimals like 0.8660, saves readers from retyping each value.

• Fix the decimal count so right-aligned digits line up

  GFM aligns the edge of the cell, not the decimal point, so 0.5 above 0.8660 looks ragged even when right-aligned. Give every decimal in a column the same number of places (0.5000, 0.7071, 0.8660); centered exact values, as in this template, need no such padding.

What Goes in Each Column

How to Fill It In

1. 1Decide the scope first: the first quadrant for a quick reference, every multiple of 30° and 45° from 0° to 330° for a full unit circle. Add a decimal column only if readers will use the values in code or measurements.
2. 2Derive the exact values from the two special triangles and the quadrant sign rules instead of copying from another table. Reduce every fraction and settle on rationalized or unrationalized denominators before you start.
3. 3Choose notation for your renderer. Unicode in code spans (√3/2) displays everywhere; GitHub renders $...$ math inside table cells (see math and LaTeX in tables). For a paper, export the finished table with the Markdown to LaTeX converter.
4. 4Verify numerically with a short script: compute Math.sin(deg * Math.PI / 180) for each row and compare with the decimal value of your exact entry to within about 1e-12. Typos in radicals show up immediately.
5. 5Run the identity checks before publishing: sin² θ + cos² θ = 1 in every row, tan θ = sin θ / cos θ wherever cosine is non-zero, and signs match the quadrant.

Ready-to-Paste Variations

| Angle | Radians | sin | cos | tan |
| :---: | :---: | :---: | :---: | :---: |
| 120° | $\frac{2\pi}{3}$ | $\frac{\sqrt{3}}{2}$ | $-\frac{1}{2}$ | $-\sqrt{3}$ |
| 135° | $\frac{3\pi}{4}$ | $\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $-1$ |
| 150° | $\frac{5\pi}{6}$ | $\frac{1}{2}$ | $-\frac{\sqrt{3}}{2}$ | $-\frac{\sqrt{3}}{3}$ |
| 210° | $\frac{7\pi}{6}$ | $-\frac{1}{2}$ | $-\frac{\sqrt{3}}{2}$ | $\frac{\sqrt{3}}{3}$ |
| 225° | $\frac{5\pi}{4}$ | $-\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $1$ |
| 240° | $\frac{4\pi}{3}$ | $-\frac{\sqrt{3}}{2}$ | $-\frac{1}{2}$ | $\sqrt{3}$ |
| 270° | $\frac{3\pi}{2}$ | $-1$ | $0$ | undefined |
| 300° | $\frac{5\pi}{3}$ | $-\frac{\sqrt{3}}{2}$ | $\frac{1}{2}$ | $-\sqrt{3}$ |
| 315° | $\frac{7\pi}{4}$ | $-\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $-1$ |
| 330° | $\frac{11\pi}{6}$ | $-\frac{1}{2}$ | $\frac{\sqrt{3}}{2}$ | $-\frac{\sqrt{3}}{3}$ |

| Angle | sin | cos | tan |
| :---: | ---: | ---: | ---: |
| 0° | 0.0000000000 | 1.0000000000 | 0.0000000000 |
| 30° | 0.5000000000 | 0.8660254038 | 0.5773502692 |
| 45° | 0.7071067812 | 0.7071067812 | 1.0000000000 |
| 60° | 0.8660254038 | 0.5000000000 | 1.7320508076 |
| 90° | 1.0000000000 | 0.0000000000 | undefined |

| Constant | Symbol | Value | JavaScript | Python |
| :--- | :---: | :--- | :--- | :--- |
| Pi | $\pi$ | 3.14159265358979… | `Math.PI` | `math.pi` |
| Tau | $\tau = 2\pi$ | 6.28318530717958… | `2 * Math.PI` | `math.tau` |
| Euler’s number | $e$ | 2.71828182845904… | `Math.E` | `math.e` |
| Golden ratio | $\varphi$ | 1.61803398874989… | `(1 + Math.sqrt(5)) / 2` | `(1 + math.sqrt(5)) / 2` |
| Square root of 2 | $\sqrt{2}$ | 1.41421356237309… | `Math.SQRT2` | `math.sqrt(2)` |
| Natural log of 2 | $\ln 2$ | 0.69314718055994… | `Math.LN2` | `math.log(2)` |
| One degree in radians | $\pi/180$ | 0.01745329251994… | `Math.PI / 180` | `math.radians(1)` |

Common Mistakes

• Passing degrees to functions that expect radians.

  Math.sin, Python’s math.sin, and GLSL’s sin all take radians, so Math.sin(90) is about 0.894, not 1. Convert with deg * Math.PI / 180 (or math.radians) and label both angle columns so readers know which unit a value is in.

• Expecting floating-point code to return the exact zeros in the table.

  Math.sin(Math.PI) returns about 1.22e-16 because Math.PI is not exactly π. Compare against table values with a tolerance such as Math.abs(a - b) < 1e-12 instead of ===.

• Writing ∞ or a number for tan 90°.

  Tangent is undefined there because cosine is zero, and the limit is +∞ from one side and −∞ from the other. Write “undefined” for 90° and 270° and keep the rows, since readers look up exactly those angles.

• Using |x| for absolute values or norms inside a table cell.

  The pipe ends the cell even inside $...$ math. Write \lvert x \rvert or \vert x \vert in LaTeX, or escape the character as described in escaping pipes.