Значения тригонометрических функций

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

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


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