Значения тригонометрических функций
Значения тригонометрических функций для основных углов: \(0^\circ\), \(30^\circ\), \(45^\circ\), \(60^\circ\), \(90^\circ\), \(120^\circ\), \(180^\circ\), \(270^\circ\) и \(360^\circ\)
| \(\alpha^\circ\) | \(\alpha\) рад | \(\sin \alpha\) | \(\cos \alpha\) | \(\tan \alpha\) | \(\cot \alpha\) | \(\sec \alpha\) | \(\csc \alpha\) |
|---|---|---|---|---|---|---|---|
| \(0^\circ\) | \(0\) | \(0\) | \(1\) | \(0\) | \(\infty\) | \(1\) | \(\infty\) |
| \(30^\circ\) | \(\pi/6\) | \(1/2\) | \(\sqrt 3/2\) | \(1/\sqrt 3\) | \(\sqrt 3\) | \(2/\sqrt 3\) | \(2\) |
| \(45^\circ\) | \(\pi/4\) | \(\sqrt 2/2\) | \(\sqrt 2/2\) | \(1\) | \(1\) | \(\sqrt 2\) | \(\sqrt 2\) |
| \(60^\circ\) | \(\pi/3\) | \(\sqrt 3/2\) | \(1/2\) | \(\sqrt 3\) | \(1/\sqrt 3\) | \(2\) | \(2/\sqrt 3\) |
| \(90^\circ\) | \(\pi/2\) | \(1\) | \(0\) | \(\infty \) | \(0\) | \(\infty\) | \(1\) |
| \(120^\circ\) | \(2\pi/3\) | \(\sqrt 3/2\) | \(-1/2\) | \(-\sqrt 3\) | \(-1/\sqrt 3\) | \(-2\) | \(2/\sqrt 3\) |
| \(180^\circ\) | \(\pi\) | \(0\) | \(-1\) | \(0\) | \(\infty\) | \(-1\) | \(\infty\) |
| \(270^\circ\) | \(3\pi/2\) | \(-1\) | \(0\) | \(\infty\) | \(0\) | \(\infty\) | \(-1\) |
| \(360^\circ\) | \(2\pi\) | \(0\) | \(1\) | \(0\) | \(\infty\) | \(1\) | \(\infty\) |
Значения тригонометрических функций для некоторых нестандартных углов: \(15^\circ\), \(18^\circ\), \(36^\circ\), \(54^\circ\), \(72^\circ\) и \(75^\circ\)
| \(\alpha^\circ\) | \(\alpha\) рад | \(\sin \alpha\) | \(\cos \alpha\) | \(\tan \alpha\) | \(\cot \alpha\) |
|---|---|---|---|---|---|
| \(15^\circ\) | \(\pi/12\) | \(\large\frac{{\sqrt 6 - \sqrt 2 }}{4}\normalsize\) | \(\large\frac{{\sqrt 6 + \sqrt 2 }}{4}\normalsize\) | \(2 - \sqrt 3\) | \(2 + \sqrt 3\) |
| \(18^\circ\) | \(\pi/10\) | \(\large\frac{{\sqrt 5 - 1}}{4}\normalsize\) | \(\large\frac{{\sqrt {10 + 2\sqrt 5 } }}{4}\normalsize\) | \(\large\sqrt {\frac{{5 - 2\sqrt 5 }}{5}}\normalsize\) | \(\sqrt {5 + 2\sqrt 5 }\) |
| \(36^\circ\) | \(\pi/5\) | \(\large\frac{{\sqrt {10 - 2\sqrt 5 } }}{4}\normalsize\) | \(\large\frac{{\sqrt 5 + 1}}{4}\normalsize\) | \(\large\frac{{\sqrt {10 - 2\sqrt 5 } }}{{\sqrt 5 + 1}}\normalsize\) | \(\large\frac{{\sqrt 5 + 1}}{{\sqrt {10 - 2\sqrt 5 } }}\normalsize\) |
| \(54^\circ\) | \(3\pi/10\) | \(\large\frac{{\sqrt 5 + 1}}{4}\normalsize\) | \(\large\frac{{\sqrt {10 - 2\sqrt 5 } }}{4}\normalsize\) | \(\large\frac{{\sqrt 5 + 1}}{{\sqrt {10 - 2\sqrt 5 } }}\normalsize\) | \(\large\frac{{\sqrt {10 - 2\sqrt 5 } }}{{\sqrt 5 + 1}}\normalsize\) |
| \(72^\circ\) | \(2\pi/5\) | \(\large\frac{{\sqrt {10 + 2\sqrt 5 } }}{4}\normalsize\) | \(\large\frac{{\sqrt 5 - 1}}{4}\normalsize\) | \(\sqrt {5 + 2\sqrt 5 }\) | \(\large\sqrt {\frac{{5 - 2\sqrt 5 }}{5}}\normalsize\) |
| \(75^\circ\) | \(5\pi/12\) | \(\large\frac{{\sqrt 6 + \sqrt 2 }}{4}\normalsize\) | \(\large\frac{{\sqrt 6 - \sqrt 2 }}{4}\normalsize\) | \(2 + \sqrt 3\) | \(2 - \sqrt 3\) |