Значения тригонометрических функций
Величины углов (аргументы функций): \(\alpha\) Тригонометрические функции: \(\sin \alpha\), \(\cos \alpha\), \(\tan \alpha\), \(\cot \alpha\), \(\sec \alpha\), \(\csc \alpha\)

  1. Значения тригонометрических функций для основных углов: \(0^\circ\), \(30^\circ\), \(45^\circ\), \(60^\circ\), \(90^\circ\), \(120^\circ\), \(180^\circ\), \(270^\circ\) и \(360^\circ\)

    2. \(\alpha^\circ\)
    \(\alpha\) рад
    \(\sin \alpha\)
    \(\cos \alpha\)
    \(\tan \alpha\)
    \(\cot \alpha\)
    \(\sec \alpha\)
    \(\csc \alpha\)
    \(0^\circ\)
    \(0\)
    \(0\)
    \(1\)
    \(0\)
    \(\infty\)
    \(1\)
    \(\infty\)
    \(30^\circ\)
    \(\pi/6\)
    \(1/2\)
    \(\sqrt 3/2\)
    \(1/\sqrt 3\)
    \(\sqrt 3\)
    \(2/\sqrt 3\)
    \(2\)
    \(45^\circ\)
    \(\pi/4\)
    \(\sqrt 2/2\)
    \(\sqrt 2/2\)
    \(1\)
    \(1\)
    \(\sqrt 2\)
    \(\sqrt 2\)
    \(60^\circ\)
    \(\pi/3\)
    \(\sqrt 3/2\)
    \(1/2\)
    \(\sqrt 3\)
    \(1/\sqrt 3\)
    \(2\)
    \(2/\sqrt 3\)
    \(90^\circ\)
    \(\pi/2\)
    \(1\)
    \(0\)
    \(\infty \)
    \(0\)
    \(\infty\)
    \(1\)
    \(120^\circ\)
    \(2\pi/3\)
    \(\sqrt 3/2\)
    \(-1/2\)
    \(-\sqrt 3\)
    \(-1/\sqrt 3\)
    \(-2\)
    \(2/\sqrt 3\)
    \(180^\circ\)
    \(\pi\)
    \(0\)
    \(-1\)
    \(0\)
    \(\infty\)
    \(-1\)
    \(\infty\)
    \(270^\circ\)
    \(3\pi/2\)
    \(-1\)
    \(0\)
    \(\infty\)
    \(0\)
    \(\infty\)
    \(-1\)
    \(360^\circ\)
    \(2\pi\)
    \(0\)
    \(1\)
    \(0\)
    \(\infty\)
    \(1\)
    \(\infty\)

  2. Значения тригонометрических функций для некоторых нестандартных углов: \(15^\circ\), \(18^\circ\), \(36^\circ\), \(54^\circ\), \(72^\circ\) и \(75^\circ\)

    3. \(\alpha^\circ\)
    \(\alpha\) рад
    \(\sin \alpha\)
    \(\cos \alpha\)
    \(\tan \alpha\)
    \(\cot \alpha\)
    \(15^\circ\)
    \(\pi/12\)
    \(\large\frac{{\sqrt 6 - \sqrt 2 }}{4}\normalsize\)
    \(\large\frac{{\sqrt 6 + \sqrt 2 }}{4}\normalsize\)
    \(2 - \sqrt 3\)
    \(2 + \sqrt 3\)
    \(18^\circ\)
    \(\pi/10\)
    \(\large\frac{{\sqrt 5 - 1}}{4}\normalsize\)
    \(\large\frac{{\sqrt {10 + 2\sqrt 5 } }}{4}\normalsize\)
    \(\large\sqrt {\frac{{5 - 2\sqrt 5 }}{5}}\normalsize\)
    \(\sqrt {5 + 2\sqrt 5 }\)
    \(36^\circ\)
    \(\pi/5\)
    \(\large\frac{{\sqrt {10 - 2\sqrt 5 } }}{4}\normalsize\)
    \(\large\frac{{\sqrt 5 + 1}}{4}\normalsize\)
    \(\large\frac{{\sqrt {10 - 2\sqrt 5 } }}{{\sqrt 5 + 1}}\normalsize\)
    \(\large\frac{{\sqrt 5 + 1}}{{\sqrt {10 - 2\sqrt 5 } }}\normalsize\)
    \(54^\circ\)
    \(3\pi/10\)
    \(\large\frac{{\sqrt 5 + 1}}{4}\normalsize\)
    \(\large\frac{{\sqrt {10 - 2\sqrt 5 } }}{4}\normalsize\)
    \(\large\frac{{\sqrt 5 + 1}}{{\sqrt {10 - 2\sqrt 5 } }}\normalsize\)
    \(\large\frac{{\sqrt {10 - 2\sqrt 5 } }}{{\sqrt 5 + 1}}\normalsize\)
    \(72^\circ\)
    \(2\pi/5\)
    \(\large\frac{{\sqrt {10 + 2\sqrt 5 } }}{4}\normalsize\)
    \(\large\frac{{\sqrt 5 - 1}}{4}\normalsize\)
    \(\sqrt {5 + 2\sqrt 5 }\)
    \(\large\sqrt {\frac{{5 - 2\sqrt 5 }}{5}}\normalsize\)
    \(75^\circ\)
    \(5\pi/12\)
    \(\large\frac{{\sqrt 6 + \sqrt 2 }}{4}\normalsize\)
    \(\large\frac{{\sqrt 6 - \sqrt 2 }}{4}\normalsize\)
    \(2 + \sqrt 3\)
    \(2 - \sqrt 3\)