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