次の表は、角度 \(x\) を \(0\) から \(2\pi\) まで \( \frac{\pi}{6} \) ごとに分割し、それぞれの三角関数の値を示します：
| 三角関数 | \(0\) | \(\frac{\pi}{6}\) | \(\frac{\pi}{4}\) | \(\frac{\pi}{3}\) | \(\frac{\pi}{2}\) | \(\frac{2\pi}{3}\) | \(\frac{3\pi}{4}\) | \(\frac{5\pi}{6}\) | \(\pi\) | \(\frac{7\pi}{6}\) | \(\frac{5\pi}{4}\) | \(\frac{4\pi}{3}\) | \(\frac{3\pi}{2}\) | \(\frac{5\pi}{3}\) | \(\frac{7\pi}{4}\) | \(\frac{11\pi}{6}\) | \(2\pi\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\sin x\) | 0 | \(\frac{1}{2}\) | \(\frac{\sqrt{2}}{2}\) | \(\frac{\sqrt{3}}{2}\) | 1 | \(\frac{\sqrt{3}}{2}\) | \(\frac{\sqrt{2}}{2}\) | \(\frac{1}{2}\) | 0 | -\(\frac{1}{2}\) | -\(\frac{\sqrt{2}}{2}\) | -\(\frac{\sqrt{3}}{2}\) | -1 | -\(\frac{\sqrt{3}}{2}\) | -\(\frac{\sqrt{2}}{2}\) | -\(\frac{1}{2}\) | 0 |
| \(\cos x\) | 1 | \(\frac{\sqrt{3}}{2}\) | \(\frac{\sqrt{2}}{2}\) | \(\frac{1}{2}\) | 0 | -\(\frac{1}{2}\) | -\(\frac{\sqrt{2}}{2}\) | -\(\frac{\sqrt{3}}{2}\) | -1 | -\(\frac{\sqrt{3}}{2}\) | -\(\frac{\sqrt{2}}{2}\) | -\(\frac{1}{2}\) | 0 | \(\frac{1}{2}\) | \(\frac{\sqrt{2}}{2}\) | \(\frac{\sqrt{3}}{2}\) | 1 |
| \(\tan x\) | 0 | \(\frac{1}{\sqrt{3}}\) | 1 | \(\sqrt{3}\) | \(\text{undefined}\) | -\(\sqrt{3}\) | -1 | -\(\frac{1}{\sqrt{3}}\) | 0 | \(\frac{1}{\sqrt{3}}\) | 1 | \(\sqrt{3}\) | \(\text{undefined}\) | -\(\sqrt{3}\) | -1 | \(\frac{1}{\sqrt{3}}\) | 0 |
| \(\csc x\) | \(\text{undefined}\) | 2 | \(\sqrt{2}\) | \(\frac{2}{\sqrt{3}}\) | 1 | \(\frac{2}{\sqrt{3}}\) | \(\sqrt{2}\) | 2 | \(\text{undefined}\) | -2 | -\(\sqrt{2}\) | -\(\frac{2}{\sqrt{3}}\) | -1 | -\(\frac{2}{\sqrt{3}}\) | -\(\sqrt{2}\) | -2 | \(\text{undefined}\) |
| \(\sec x\) | 1 | \(\frac{2}{\sqrt{3}}\) | \(\sqrt{2}\) | 2 | \(\text{undefined}\) | -2 | -\(\sqrt{2}\) | -\(\frac{2}{\sqrt{3}}\) | -1 | -\(\frac{2}{\sqrt{3}}\) | -\(\sqrt{2}\) | -2 | \(\text{undefined}\) | 2 | \(\sqrt{2}\) | \(\frac{2}{\sqrt{3}}\) | 1 |
| \(\cot x\) | \(\text{undefined}\) | \(\sqrt{3}\) | 1 | \(\frac{1}{\sqrt{3}}\) | 0 | \(\frac{1}{\sqrt{3}}\) | 1 | \(\sqrt{3}\) | \(\text{undefined}\) | \(\frac{1}{\sqrt{3}}\) | 1 | \(\sqrt{3}\) | 0 | \(\frac{1}{\sqrt{3}}\) | 1 | \(\sqrt{3}\) | \(\text{undefined}\) |
以下は、逆三角関数の定義域に基づいた代表値です：
| 値 | \(\arcsin x\) | \(\arccos x\) | \(\arctan x\) |
|---|---|---|---|
| \(-1\) | \(-\frac{\pi}{2}\) | \(\pi\) | \(-\frac{\pi}{4}\) |
| \(-\frac{\sqrt{3}}{2}\) | – | – | – |
| \(-\frac{1}{\sqrt{3}}\) | – | – | \(-\frac{\pi}{6}\) |
| \(-\frac{1}{2}\) | \(-\frac{\pi}{6}\) | \(\frac{5\pi}{6}\) | – |
| 0 | 0 | \(\frac{\pi}{2}\) | 0 |
| \(\frac{1}{2}\) | \(\frac{\pi}{6}\) | \(\frac{5\pi}{6}\) | – |
| \(\frac{1}{\sqrt{3}}\) | – | – | \(\frac{\pi}{6}\) |
| \(\frac{\sqrt{2}}{2}\) | \(\frac{\pi}{4}\) | \(\frac{\pi}{4}\) | – |
| \(\frac{\sqrt{3}}{2}\) | \(\frac{\pi}{3}\) | \(\frac{\pi}{6}\) | – |
| 1 | \(\frac{\pi}{2}\) | 0 | \(\frac{\pi}{4}\) |
| \(\sqrt{3}\) | – | – | \(\frac{\pi}{3}\) |