Значения тригонометрических функций

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

α∘\alpha^\circα\alpha радsin⁡α\sin \alphacos⁡α\cos \alphatan⁡α\tan \alphacot⁡α\cot \alphasec⁡α\sec \alphacsc⁡α\csc \alpha
0∘0^\circ00001100∞\infty11∞\infty
30∘30^\circπ/6\pi/61/21/23/2\sqrt 3/21/31/\sqrt 33\sqrt 32/32/\sqrt 322
45∘45^\circπ/4\pi/42/2\sqrt 2/22/2\sqrt 2/211112\sqrt 22\sqrt 2
60∘60^\circπ/3\pi/33/2\sqrt 3/21/21/23\sqrt 31/31/\sqrt 3222/32/\sqrt 3
90∘90^\circπ/2\pi/21100∞\infty 00∞\infty11
120∘120^\circ2π/32\pi/33/2\sqrt 3/2−1/2-1/2−3-\sqrt 3−1/3-1/\sqrt 3−2-22/32/\sqrt 3
180∘180^\circπ\pi00−1-100∞\infty−1-1∞\infty
270∘270^\circ3π/23\pi/2−1-100∞\infty00∞\infty−1-1
360∘360^\circ2π2\pi001100∞\infty11∞\infty

Значения тригонометрических функций для некоторых нестандартных углов: 15∘15^\circ, 18∘18^\circ, 36∘36^\circ, 54∘54^\circ, 72∘72^\circ и 75∘75^\circ  

α∘\alpha^\circα\alpha радsin⁡α\sin \alphacos⁡α\cos \alphatan⁡α\tan \alphacot⁡α\cot \alpha
15∘15^\circπ/12\pi/126−24\large\frac{{\sqrt 6 - \sqrt 2 }}{4}\normalsize6+24\large\frac{{\sqrt 6 + \sqrt 2 }}{4}\normalsize2−32 - \sqrt 32+32 + \sqrt 3
18∘18^\circπ/10\pi/105−14\large\frac{{\sqrt 5 - 1}}{4}\normalsize10+254\large\frac{{\sqrt {10 + 2\sqrt 5 } }}{4}\normalsize5−255\large\sqrt {\frac{{5 - 2\sqrt 5 }}{5}}\normalsize5+25\sqrt {5 + 2\sqrt 5 }
36∘36^\circπ/5\pi/510−254\large\frac{{\sqrt {10 - 2\sqrt 5 } }}{4}\normalsize5+14\large\frac{{\sqrt 5 + 1}}{4}\normalsize10−255+1\large\frac{{\sqrt {10 - 2\sqrt 5 } }}{{\sqrt 5 + 1}}\normalsize5+110−25\large\frac{{\sqrt 5 + 1}}{{\sqrt {10 - 2\sqrt 5 } }}\normalsize
54∘54^\circ3π/103\pi/105+14\large\frac{{\sqrt 5 + 1}}{4}\normalsize10−254\large\frac{{\sqrt {10 - 2\sqrt 5 } }}{4}\normalsize5+110−25\large\frac{{\sqrt 5 + 1}}{{\sqrt {10 - 2\sqrt 5 } }}\normalsize10−255+1\large\frac{{\sqrt {10 - 2\sqrt 5 } }}{{\sqrt 5 + 1}}\normalsize
72∘72^\circ2π/52\pi/510+254\large\frac{{\sqrt {10 + 2\sqrt 5 } }}{4}\normalsize5−14\large\frac{{\sqrt 5 - 1}}{4}\normalsize5+25\sqrt {5 + 2\sqrt 5 }5−255\large\sqrt {\frac{{5 - 2\sqrt 5 }}{5}}\normalsize
75∘75^\circ5π/125\pi/126+24\large\frac{{\sqrt 6 + \sqrt 2 }}{4}\normalsize6−24\large\frac{{\sqrt 6 - \sqrt 2 }}{4}\normalsize2+32 + \sqrt 32−32 - \sqrt 3
Тригонометрия Математика Тригонометрия Формулы Теория
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