Значения тригонометрических функций (sin, cos, tan, cot) для разных аргументов и промежутки знакопостоянства: таблицы и правила определения знаков.
Для \(x\in\left[0,\;\pi\right]\):
| \(x\) | \(0\) | \(\frac{\pi}{6}\) | \(\frac{\pi}{4}\) | \(\frac{\pi}{3}\) | \(\frac{\pi}{2}\) | \(\frac{2\pi}{3}\) | \(\frac{3\pi}{4}\) | \(\frac{5\pi}{6}\) | \(\pi\) |
| \(\sin x\) | \(0\) | \(\frac{1}{2}\) | \(\frac{\sqrt{2}}{2}\) | \(\frac{\sqrt{3}}{2}\) | \(1\) | \(\frac{\sqrt{3}}{2}\) | \(\frac{\sqrt{2}}{2}\) | \(\frac{1}{2}\) | \(0\) |
| \(\cos x\) | \(1\) | \(\frac{\sqrt{3}}{2}\) | \(\frac{\sqrt{2}}{2}\) | \(\frac{1}{2}\) | \(0\) | \(-\frac{1}{2}\) | \(-\frac{\sqrt{2}}{2}\) | \(-\frac{\sqrt{3}}{2}\) | \(-1\) |
| \(\tan x\) | \(0\) | \(\frac{1}{\sqrt{3}}\) | \(1\) | \(\sqrt{3}\) | \(-\) | \(-\sqrt{3}\) | \(-1\) | \(-\frac{1}{\sqrt{3}}\) | \(0\) |
| \(\cot x\) | \(-\) | \(\sqrt{3}\) | \(1\) | \(\frac{1}{\sqrt{3}}\) | \(0\) | \(-\frac{1}{\sqrt{3}}\) | \(-1\) | \(-\sqrt{3}\) | \(-\) |
Для \(x\in\left[\tfrac{7\pi}{6},\;2\pi\right]\):
| \(x\) | \(\frac{7\pi}{6}\) | \(\frac{5\pi}{4}\) | \(\frac{4\pi}{3}\) | \(\frac{3\pi}{2}\) | \(\frac{5\pi}{3}\) | \(\frac{7\pi}{4}\) | \(\frac{11\pi}{6}\) | \(2\pi\) |
| \(\sin x\) | \(-\frac{1}{2}\) | \(-\frac{\sqrt{2}}{2}\) | \(-\frac{\sqrt{3}}{2}\) | \(-1\) | \(-\frac{\sqrt{3}}{2}\) | \(-\frac{\sqrt{2}}{2}\) | \(-\frac{1}{2}\) | \(0\) |
| \(\cos x\) | \(-\frac{\sqrt{3}}{2}\) | \(-\frac{\sqrt{2}}{2}\) | \(-\frac{1}{2}\) | \(0\) | \(\frac{1}{2}\) | \(\frac{\sqrt{2}}{2}\) | \(\frac{\sqrt{3}}{2}\) | \(1\) |
| \(\tan x\) | \(\frac{1}{\sqrt{3}}\) | \(1\) | \(\sqrt{3}\) | \(-\) | \(-\sqrt{3}\) | \(-1\) | \(-\frac{1}{\sqrt{3}}\) | \(0\) |
| \(\cot x\) | \(\sqrt{3}\) | \(1\) | \(\frac{1}{\sqrt{3}}\) | \(0\) | \(-\frac{1}{\sqrt{3}}\) | \(-1\) | \(-\sqrt{3}\) | \(-\) |
Промежутки знакопостоянства тригонометрических функций