三角函数对照表

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三角函数对照表

三角函数SINCOSTAN三角函数SINCOSTAN

0°01090°10无

1°0.01740.99980.017489°0.99980.017457.2899

2°0.03480.99930.034988°0.99930.034828.6362

3°0.05230.99860.052487°0.99860.052319.0811

4°0.06970.99750.069986°0.99750.069714.3006

5°0.08710.99610.087485°0.99610.087111.4300

6°0.10450.99450.105184°0.99450.10459.5143

7°0.12180.99250.122783°0.99250.12188.1443

8°0.13910.99020.140582°0.99020.13917.1153

9°0.15640.98760.158381°0.98760.15646.3137

10°0.17360.98480.176380°0.98480.17365.6712

11°0.19080.98160.194379°0.98160.19085.1445

12°0.20790.97810.212578°0.97810.20794.7046

13°0.22490.97430.230877°0.97430.22494.3314

14°0.24190.97020.249376°0.97020.24194.0107

15°0.25880.96590.267975°0.96590.25883.7320

16°0.27560.96120.286774°0.96120.27563.4874

17°0.29230.95630.305773°0.95630.29233.2708

18°0.30900.95100.324972°0.95100.30903.0776

19°0.32550.94550.344371°0.94550.32552.9042

20°0.34200.93960.363970°0.93960.34202.7474

21°0.35830.93350.383869°0.93350.35832.6050

22°0.37460.92710.404068°0.92710.37462.4750

23°0.39070.92050.424467°0.92050.39072.3558

24°0.40670.91350.445266°0.91350.40672.2460

25°0.42260.90630.466365°0.90630.42262.1445

26°0.43830.89870.487764°0.89870.43832.0503

27°0.45390.89100.509563°0.89100.45391.9626

28°0.46940.88290.531762°0.88290.46941.8807

29°0.48480.87460.554361°0.87460.48481.8040

30°0.50000.86600.577360°0.86600.50001.7320

31°0.51500.85710.600859°0.85710.51501.6642

32°0.52990.84800.624858°0.84800.52991.6003

33°0.54460.83860.649457°0.83860.54461.5398

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34°0.55910.82900.674556°0.82900.55911.4825

35°0.57350.81910.700255°0.81910.57351.4281

36°0.58770.80900.726554°0.80900.58771.3763

37°0.60180.79860.753553°0.79860.60181.3270

38°0.61560.78800.781252°0.78800.61561.2799

39°0.62930.77710.809751°0.77710.62931.2348

40°0.64270.76600.839050°0.76600.64271.1917

41°0.65600.75470.869249°0.75470.65601.1503

42°0.66910.74310.900448°0.74310.66911.1106

43°0.68190.73130.932547°0.73130.68191.0723

44°0.69460.71930.965646°0.71930.69461.0355

45°0.70710.7071145°0.70710.70711

同角基本关系式

倒数关系商的关系平方关系

tancot1

sincsc1

cosc1













sinc

tan

coscsc

coscsc

cot

sinc

















22

22

22

sincos1

1tanc

1cotcsc













诱导公式

sin()sincos()costan()tancot()cot

sin()cos

2

cos()sin

2

tan()cot

2

cot()tan

2

























sin()sin

cos()cos

tan()tan

cot()cot

















3

sin()cos

2

3

cos()sin

2

3

tan()cot

2

3

cot()tan

2

























sin(2)sin

cos(2)cos

tan(2)tan

cot(2)cot

















(其中k∈Z)

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3/4

sin()cos

2

cos()sin

2

tan()cot

2

cot()tan

2

























sin()sin

cos()cos

tan()tan

cot()cot

















3

sin()cos

2

3

cos()sin

2

3

tan()cot

2

3

cot()tan

2

























sin(2)sin

cos(2)cos

tan(2)tan

cot(2)cot

















两角和与差的三角函数公式万能公式

sin()sincoscossin

sin()sincoscossin

cos()coscossinsin

cos()coscossinsin

















tantan

tan()

1tantan













tantan

tan()

1tantan













2tan(/2)

sin

1tan2(/2)











1tan2(/2)

cos

1tan2(/2)













2tan(/2)

tan

1tan2(/2)











半角的正弦、余弦和正切公式三角函数的降幂公式

1cos

sin()

22

1cos

cos()

22

1cos1cossin

tan()

21cossin1cos























2

2

1cos2

sin

2

1cos2

cos

2

















二倍角的正弦、余弦和正切公式三倍角的正弦、余弦和正切公式

sin22sincos

cos2cos2sin22cos2112sin2









2tan

tan2

1tan2











sin33sin4sin3

cos34cos33cos.

3tantan3

tan3

13tan2





















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三角函数的和差化积公式三角函数的积化和差公式

sinsin2sincos

22

sinsin2cossin

22

coscos2coscos

22

coscos2sinsin

22









































1

sincossin()sin()

2

1

cossinsin()sin()

2

1

coscoscos()cos()

2

1

sinsincos()cos()

2

















化asinα±bcosα为一个角的一个三角函数的形式（辅助角的三角函数的公式）

22sincossin()axbxabx

其中角所在的象限由a、

b

的符号确定，角的值由

tan

b

a

确定

六边形记忆法：图形结构“上弦中切下割，

左正右余中间1”；记忆方法“对角线上两个

函数的积为1；阴影三角形上两顶点的三角函

数值的平方和等于下顶点的三角函数值的平

方；任意一顶点的三角函数值等于相邻两个

顶点的三角函数值的乘积。”