0°～90° 锐角三角函数值（可化简为实数根式，其余用复数根式表示）

约定： $i=\sqrt{-1}$，$\zeta_n = \sqrt[360]{1^{\,n}}$

0°

$\cos0^\circ = 1,\quad \sin0^\circ = 0$

1°

$\cos1^\circ = \dfrac{\zeta_1+\zeta_{359}}{2},\quad \sin1^\circ = \dfrac{\zeta_1-\zeta_{359}}{2i}$

2°

$\cos2^\circ = \dfrac{\zeta_2+\zeta_{358}}{2},\quad \sin2^\circ = \dfrac{\zeta_2-\zeta_{358}}{2i}$

3°

$\cos3^\circ = \dfrac{\sqrt{30+6\sqrt5}+\sqrt{10+2\sqrt5}-\sqrt5-1}{8},\quad \sin3^\circ = \dfrac{\sqrt{10-2\sqrt5}+\sqrt5+1}{8}\sqrt{2+\sqrt2}$

4°

$\cos4^\circ = \dfrac{\zeta_4+\zeta_{356}}{2},\quad \sin4^\circ = \dfrac{\zeta_4-\zeta_{356}}{2i}$

5°

$\cos5^\circ = \dfrac{\sqrt{10+2\sqrt5}+\sqrt5+1}{8}\sqrt{2+\sqrt2},\quad \sin5^\circ = \dfrac{\sqrt{30-6\sqrt5}+\sqrt{10-2\sqrt5}}{8}$

6°

$\cos6^\circ = \dfrac{\sqrt{10+2\sqrt5}+\sqrt{15}+\sqrt3}{8},\quad \sin6^\circ = \dfrac{\sqrt{15}-\sqrt3+\sqrt{10-2\sqrt5}}{8}$

7°

$\cos7^\circ = \dfrac{\zeta_7+\zeta_{353}}{2},\quad \sin7^\circ = \dfrac{\zeta_7-\zeta_{353}}{2i}$

8°

$\cos8^\circ = \dfrac{\zeta_8+\zeta_{352}}{2},\quad \sin8^\circ = \dfrac{\zeta_8-\zeta_{352}}{2i}$

9°

$\cos9^\circ = \dfrac{\sqrt{10+2\sqrt5}+\sqrt{10-2\sqrt5}}{4},\quad \sin9^\circ = \dfrac{\sqrt{10+2\sqrt5}-\sqrt{10-2\sqrt5}}{4}$

10°

$\cos10^\circ = \dfrac{\zeta_{10}+\zeta_{350}}{2},\quad \sin10^\circ = \dfrac{\zeta_{10}-\zeta_{350}}{2i}$

11°

$\cos11^\circ = \dfrac{\zeta_{11}+\zeta_{349}}{2},\quad \sin11^\circ = \dfrac{\zeta_{11}-\zeta_{349}}{2i}$

12°

$\cos12^\circ = \dfrac{\sqrt{10+2\sqrt5}+\sqrt{15}-\sqrt3}{8},\quad \sin12^\circ = \dfrac{\sqrt{15}+\sqrt3-\sqrt{10-2\sqrt5}}{8}$

13°

$\cos13^\circ = \dfrac{\zeta_{13}+\zeta_{347}}{2},\quad \sin13^\circ = \dfrac{\zeta_{13}-\zeta_{347}}{2i}$

14°

$\cos14^\circ = \dfrac{\zeta_{14}+\zeta_{346}}{2},\quad \sin14^\circ = \dfrac{\zeta_{14}-\zeta_{346}}{2i}$

15°

$\cos15^\circ = \dfrac{\sqrt6+\sqrt2}{4},\quad \sin15^\circ = \dfrac{\sqrt6-\sqrt2}{4}$

16°

$\cos16^\circ = \dfrac{\zeta_{16}+\zeta_{344}}{2},\quad \sin16^\circ = \dfrac{\zeta_{16}-\zeta_{344}}{2i}$

17°

$\cos17^\circ = \dfrac{\zeta_{17}+\zeta_{343}}{2},\quad \sin17^\circ = \dfrac{\zeta_{17}-\zeta_{343}}{2i}$

18°

$\cos18^\circ = \dfrac{\sqrt{10+2\sqrt5}}{4},\quad \sin18^\circ = \dfrac{\sqrt5-1}{4}$

19°

$\cos19^\circ = \dfrac{\zeta_{19}+\zeta_{341}}{2},\quad \sin19^\circ = \dfrac{\zeta_{19}-\zeta_{341}}{2i}$

20°

$\cos20^\circ = \dfrac{\zeta_{20}+\zeta_{340}}{2},\quad \sin20^\circ = \dfrac{\zeta_{20}-\zeta_{340}}{2i}$

21°

$\cos21^\circ = \dfrac{\zeta_{21}+\zeta_{339}}{2},\quad \sin21^\circ = \dfrac{\zeta_{21}-\zeta_{339}}{2i}$

22°

$\cos22^\circ = \dfrac{\zeta_{22}+\zeta_{338}}{2},\quad \sin22^\circ = \dfrac{\zeta_{22}-\zeta_{338}}{2i}$

23°

$\cos23^\circ = \dfrac{\zeta_{23}+\zeta_{337}}{2},\quad \sin23^\circ = \dfrac{\zeta_{23}-\zeta_{337}}{2i}$

24°

$\cos24^\circ = \dfrac{\sqrt{10-2\sqrt5}+\sqrt{15}+\sqrt3}{8},\quad \sin24^\circ = \dfrac{\sqrt{10+2\sqrt5}+\sqrt3-\sqrt{15}}{8}$

25°

$\cos25^\circ = \dfrac{\zeta_{25}+\zeta_{335}}{2},\quad \sin25^\circ = \dfrac{\zeta_{25}-\zeta_{335}}{2i}$

26°

$\cos26^\circ = \dfrac{\zeta_{26}+\zeta_{334}}{2},\quad \sin26^\circ = \dfrac{\zeta_{26}-\zeta_{334}}{2i}$

27°

$\cos27^\circ = \dfrac{\sqrt{10+2\sqrt5}+\sqrt{10-2\sqrt5}}{4},\quad \sin27^\circ = \dfrac{\sqrt{10+2\sqrt5}-\sqrt{10-2\sqrt5}}{4}$

28°

$\cos28^\circ = \dfrac{\zeta_{28}+\zeta_{332}}{2},\quad \sin28^\circ = \dfrac{\zeta_{28}-\zeta_{332}}{2i}$

29°

$\cos29^\circ = \dfrac{\zeta_{29}+\zeta_{331}}{2},\quad \sin29^\circ = \dfrac{\zeta_{29}-\zeta_{331}}{2i}$

30°

$\cos30^\circ = \dfrac{\sqrt3}{2},\quad \sin30^\circ = \dfrac12$

31°

$\cos31^\circ = \dfrac{\zeta_{31}+\zeta_{329}}{2},\quad \sin31^\circ = \dfrac{\zeta_{31}-\zeta_{329}}{2i}$

32°

$\cos32^\circ = \dfrac{\zeta_{32}+\zeta_{328}}{2},\quad \sin32^\circ = \dfrac{\zeta_{32}-\zeta_{328}}{2i}$

33°

$\cos33^\circ = \dfrac{\zeta_{33}+\zeta_{327}}{2},\quad \sin33^\circ = \dfrac{\zeta_{33}-\zeta_{327}}{2i}$

34°

$\cos34^\circ = \dfrac{\zeta_{34}+\zeta_{326}}{2},\quad \sin34^\circ = \dfrac{\zeta_{34}-\zeta_{326}}{2i}$

35°

$\cos35^\circ = \dfrac{\zeta_{35}+\zeta_{325}}{2},\quad \sin35^\circ = \dfrac{\zeta_{35}-\zeta_{325}}{2i}$

36°

$\cos36^\circ = \dfrac{1+\sqrt5}{4},\quad \sin36^\circ = \dfrac{\sqrt{10-2\sqrt5}}{4}$

37°

$\cos37^\circ = \dfrac{\zeta_{37}+\zeta_{323}}{2},\quad \sin37^\circ = \dfrac{\zeta_{37}-\zeta_{323}}{2i}$

38°

$\cos38^\circ = \dfrac{\zeta_{38}+\zeta_{322}}{2},\quad \sin38^\circ = \dfrac{\zeta_{38}-\zeta_{322}}{2i}$

39°

$\cos39^\circ = \dfrac{\zeta_{39}+\zeta_{321}}{2},\quad \sin39^\circ = \dfrac{\zeta_{39}-\zeta_{321}}{2i}$

40°

$\cos40^\circ = \dfrac{\zeta_{40}+\zeta_{320}}{2},\quad \sin40^\circ = \dfrac{\zeta_{40}-\zeta_{320}}{2i}$

41°

$\cos41^\circ = \dfrac{\zeta_{41}+\zeta_{319}}{2},\quad \sin41^\circ = \dfrac{\zeta_{41}-\zeta_{319}}{2i}$

42°

$\cos42^\circ = \dfrac{\zeta_{42}+\zeta_{318}}{2},\quad \sin42^\circ = \dfrac{\zeta_{42}-\zeta_{318}}{2i}$

43°

$\cos43^\circ = \dfrac{\zeta_{43}+\zeta_{317}}{2},\quad \sin43^\circ = \dfrac{\zeta_{43}-\zeta_{317}}{2i}$

44°

$\cos44^\circ = \dfrac{\zeta_{44}+\zeta_{316}}{2},\quad \sin44^\circ = \dfrac{\zeta_{44}-\zeta_{316}}{2i}$

45°

$\cos45^\circ = \dfrac{\sqrt2}{2},\quad \sin45^\circ = \dfrac{\sqrt2}{2}$

46°

$\cos46^\circ = \dfrac{\zeta_{46}+\zeta_{314}}{2},\quad \sin46^\circ = \dfrac{\zeta_{46}-\zeta_{314}}{2i}$

47°

$\cos47^\circ = \dfrac{\zeta_{47}+\zeta_{313}}{2},\quad \sin47^\circ = \dfrac{\zeta_{47}-\zeta_{313}}{2i}$

48°

$\cos48^\circ = \dfrac{\sqrt{10+2\sqrt5}+\sqrt{15}-\sqrt3}{8},\quad \sin48^\circ = \dfrac{\sqrt{10-2\sqrt5}+\sqrt{15}+\sqrt3}{8}$

49°

$\cos49^\circ = \dfrac{\zeta_{49}+\zeta_{311}}{2},\quad \sin49^\circ = \dfrac{\zeta_{49}-\zeta_{311}}{2i}$

50°

$\cos50^\circ = \dfrac{\zeta_{50}+\zeta_{310}}{2},\quad \sin50^\circ = \dfrac{\zeta_{50}-\zeta_{310}}{2i}$

51°

$\cos51^\circ = \dfrac{\zeta_{51}+\zeta_{309}}{2},\quad \sin51^\circ = \dfrac{\zeta_{51}-\zeta_{309}}{2i}$

52°

$\cos52^\circ = \dfrac{\zeta_{52}+\zeta_{308}}{2},\quad \sin52^\circ = \dfrac{\zeta_{52}-\zeta_{308}}{2i}$

53°

$\cos53^\circ = \dfrac{\zeta_{53}+\zeta_{307}}{2},\quad \sin53^\circ = \dfrac{\zeta_{53}-\zeta_{307}}{2i}$

54°

$\cos54^\circ = \dfrac{\sqrt{10+2\sqrt5}}{4},\quad \sin54^\circ = \dfrac{1+\sqrt5}{4}$

55°

$\cos55^\circ = \dfrac{\zeta_{55}+\zeta_{305}}{2},\quad \sin55^\circ = \dfrac{\zeta_{55}-\zeta_{305}}{2i}$

56°

$\cos56^\circ = \dfrac{\zeta_{56}+\zeta_{304}}{2},\quad \sin56^\circ = \dfrac{\zeta_{56}-\zeta_{304}}{2i}$

57°

$\cos57^\circ = \dfrac{\zeta_{57}+\zeta_{303}}{2},\quad \sin57^\circ = \dfrac{\zeta_{57}-\zeta_{303}}{2i}$

58°

$\cos58^\circ = \dfrac{\zeta_{58}+\zeta_{302}}{2},\quad \sin58^\circ = \dfrac{\zeta_{58}-\zeta_{302}}{2i}$

59°

$\cos59^\circ = \dfrac{\zeta_{59}+\zeta_{301}}{2},\quad \sin59^\circ = \dfrac{\zeta_{59}-\zeta_{301}}{2i}$

60°

$\cos60^\circ = \dfrac12,\quad \sin60^\circ = \dfrac{\sqrt3}{2}$

61°

$\cos61^\circ = \dfrac{\zeta_{61}+\zeta_{299}}{2},\quad \sin61^\circ = \dfrac{\zeta_{61}-\zeta_{299}}{2i}$

62°

$\cos62^\circ = \dfrac{\zeta_{62}+\zeta_{298}}{2},\quad \sin62^\circ = \dfrac{\zeta_{62}-\zeta_{298}}{2i}$

63°

$\cos63^\circ = \dfrac{\sqrt{10+2\sqrt5}-\sqrt{10-2\sqrt5}}{4},\quad \sin63^\circ = \dfrac{\sqrt{10+2\sqrt5}+\sqrt{10-2\sqrt5}}{4}$

64°

$\cos64^\circ = \dfrac{\zeta_{64}+\zeta_{296}}{2},\quad \sin64^\circ = \dfrac{\zeta_{64}-\zeta_{296}}{2i}$

65°

$\cos65^\circ = \dfrac{\zeta_{65}+\zeta_{295}}{2},\quad \sin65^\circ = \dfrac{\zeta_{65}-\zeta_{295}}{2i}$

66°

$\cos66^\circ = \dfrac{\sqrt{10-2\sqrt5}+\sqrt{15}-\sqrt3}{8},\quad \sin66^\circ = \dfrac{\sqrt{10+2\sqrt5}+\sqrt{15}+\sqrt3}{8}$

67°

$\cos67^\circ = \dfrac{\zeta_{67}+\zeta_{293}}{2},\quad \sin67^\circ = \dfrac{\zeta_{67}-\zeta_{293}}{2i}$

68°

$\cos68^\circ = \dfrac{\zeta_{68}+\zeta_{292}}{2},\quad \sin68^\circ = \dfrac{\zeta_{68}-\zeta_{292}}{2i}$

69°

$\cos69^\circ = \dfrac{\zeta_{69}+\zeta_{291}}{2},\quad \sin69^\circ = \dfrac{\zeta_{69}-\zeta_{291}}{2i}$

70°

$\cos70^\circ = \dfrac{\zeta_{70}+\zeta_{290}}{2},\quad \sin70^\circ = \dfrac{\zeta_{70}-\zeta_{290}}{2i}$

71°

$\cos71^\circ = \dfrac{\zeta_{71}+\zeta_{289}}{2},\quad \sin71^\circ = \dfrac{\zeta_{71}-\zeta_{289}}{2i}$

72°

$\cos72^\circ = \dfrac{\sqrt5-1}{4},\quad \sin72^\circ = \dfrac{\sqrt{10+2\sqrt5}}{4}$

73°

$\cos73^\circ = \dfrac{\zeta_{73}+\zeta_{287}}{2},\quad \sin73^\circ = \dfrac{\zeta_{73}-\zeta_{287}}{2i}$

74°

$\cos74^\circ = \dfrac{\zeta_{74}+\zeta_{286}}{2},\quad \sin74^\circ = \dfrac{\zeta_{74}-\zeta_{286}}{2i}$

75°

$\cos75^\circ = \dfrac{\sqrt6-\sqrt2}{4},\quad \sin75^\circ = \dfrac{\sqrt6+\sqrt2}{4}$

76°

$\cos76^\circ = \dfrac{\zeta_{76}+\zeta_{284}}{2},\quad \sin76^\circ = \dfrac{\zeta_{76}-\zeta_{284}}{2i}$

77°

$\cos77^\circ = \dfrac{\zeta_{77}+\zeta_{283}}{2},\quad \sin77^\circ = \dfrac{\zeta_{77}-\zeta_{283}}{2i}$

78°

$\cos78^\circ = \dfrac{\sqrt{10-2\sqrt5}+\sqrt{15}+\sqrt3}{8},\quad \sin78^\circ = \dfrac{\sqrt{10+2\sqrt5}+\sqrt{15}-\sqrt3}{8}$

79°

$\cos79^\circ = \dfrac{\zeta_{79}+\zeta_{281}}{2},\quad \sin79^\circ = \dfrac{\zeta_{79}-\zeta_{281}}{2i}$

80°

$\cos80^\circ = \dfrac{\zeta_{80}+\zeta_{280}}{2},\quad \sin80^\circ = \dfrac{\zeta_{80}-\zeta_{280}}{2i}$

81°

$\cos81^\circ = \dfrac{\sqrt{10+2\sqrt5}-\sqrt{10-2\sqrt5}}{4},\quad \sin81^\circ = \dfrac{\sqrt{10+2\sqrt5}+\sqrt{10-2\sqrt5}}{4}$

82°

$\cos82^\circ = \dfrac{\zeta_{82}+\zeta_{278}}{2},\quad \sin82^\circ = \dfrac{\zeta_{82}-\zeta_{278}}{2i}$

83°

$\cos83^\circ = \dfrac{\zeta_{83}+\zeta_{277}}{2},\quad \sin83^\circ = \dfrac{\zeta_{83}-\zeta_{277}}{2i}$

84°

$\cos84^\circ = \dfrac{\sqrt{10-2\sqrt5}+\sqrt{15}-\sqrt3}{8},\quad \sin84^\circ = \dfrac{\sqrt{10+2\sqrt5}+\sqrt{15}+\sqrt3}{8}$

85°

$\cos85^\circ = \dfrac{\sqrt{30-6\sqrt5}-\sqrt{10-2\sqrt5}}{8},\quad \sin85^\circ = \dfrac{\sqrt{10+2\sqrt5}+\sqrt{30+6\sqrt5}}{8}$

86°

$\cos86^\circ = \dfrac{\sqrt{15}-\sqrt3-\sqrt{10-2\sqrt5}}{8},\quad \sin86^\circ = \dfrac{\sqrt{10+2\sqrt5}+\sqrt{15}+\sqrt3}{8}$

87°

$\cos87^\circ = \dfrac{\sqrt{10-2\sqrt5}+\sqrt5-1}{8}\sqrt{2+\sqrt2},\quad \sin87^\circ = \dfrac{\sqrt{30+6\sqrt5}-\sqrt{10+2\sqrt5}}{8}$

88°

$\cos88^\circ = \dfrac{\zeta_{88}+\zeta_{272}}{2},\quad \sin88^\circ = \dfrac{\zeta_{88}-\zeta_{272}}{2i}$

89°

$\cos89^\circ = \dfrac{\zeta_{89}+\zeta_{271}}{2},\quad \sin89^\circ = \dfrac{\zeta_{89}-\zeta_{271}}{2i}$

90°

$\cos90^\circ = 0,\quad \sin90^\circ = 1$