(完整版)三角函數(shù)特殊角值表

1、角度030456090120135150180270360函數(shù)角 a 的弧度0 /6/4 /3 /22 /33 /45 /63 /22sin01/2 2/23/21 3/2 2/21/20-10cos1 3/2 2/21/20-1/2- 2/2- 3/2-101tan0 3/313- 3-1- 3/3001、圖示法： 借助于下面三個圖形來記憶，即使有所遺忘也可根據(jù)圖形重新推出：sin30 =cos60° °=1 ， sin45 °=cos45°=2 ， tan30 °=cot60 °=3 ， tan 45 °=cot45 &

2、#176;=122322123130?45?60?311正弦函數(shù)sin =y/r 余弦函數(shù)cos=x/r 正切函數(shù)tan =y/x余切函數(shù)cot =x/y 正割函數(shù)sec=r/x 余割函數(shù)csc =r/y2、列表法：說明：正弦值隨角度變化，即0?30?45?60?90?變化；值從01231 變化，其余類似記憶2223、規(guī)律記憶法：觀察表中的數(shù)值特征，可總結(jié)為下列記憶規(guī)律：有界性：（銳角三角函數(shù)值都是正值）即當0° 90°時，則 0 sin 1； 0 cos 1 ； tan 0 ； cot0。 增減性：（銳角的正弦、正切值隨角度的增大而增大；余弦、余切值隨角度的增大而減?。?，

3、即當 0 A B90°時，則 sinA sinB；tanA tanB；cosA cosB；cotA cotB；特別地：若0° 45°，則 sinA cosA； tanA cotA若 45° A 90°，則 sinAcosA； tanA cotA4、口決記憶法：觀察表中的數(shù)值特征正弦、余弦值可表示為m 形式，正切、余切值可表示為m 形式，有關(guān) m 的值可歸納成23順口溜：一、二、三；三、二、一；三九二十七函數(shù)名 正弦余弦正切余切正割余割符號sin cos tan cot sec csc正弦函數(shù)sin（ A） =a/c余弦函數(shù)cos（A ）=b/c

4、正切函數(shù)tan（ A ） =a/b余切函數(shù)cot（ A ） =b/a其中 a 為對邊， b 為鄰邊， c 為斜邊三角函數(shù)對照表三角函數(shù)SINCOSTAN三角函數(shù)SINCOSTAN0°01090°10無1°0.01740.99980.017489°0.99980.017457.28992°0.03480.99930.034988°0.99930.034828.63623°0.05230.99860.052487°0.99860.052319.08114°0.06970.99750.069986°0

5、.99750.069714.30065°0.08710.99610.087485°0.99610.087111.43006°0.10450.99450.105184°0.99450.10459.51437°0.12180.99250.122783°0.99250.12188.14438°0.13910.99020.140582°0.99020.13917.11539°0.15640.98760.158381°0.98760.15646.313710°0.17360.98480.1763

6、80°0.98480.17365.671211°0.19080.98160.194379°0.98160.19085.144512°0.20790.97810.212578°0.97810.20794.704613°0.22490.97430.230877°0.97430.22494.331414°0.24190.97020.249376°0.97020.24194.010715°0.25880.96590.267975°0.96590.25883.732016°0.2756

7、0.96120.286774°0.96120.27563.487417°0.29230.95630.305773°0.95630.29233.270818°0.30900.95100.324972°0.95100.30903.077619°0.32550.94550.344371°0.94550.32552.904220°0.34200.93960.363970°0.93960.34202.747421°0.35830.93350.383869°0.93350.35832.605022

8、°0.37460.92710.404068°0.92710.37462.475023°0.39070.92050.424467°0.92050.39072.355824°0.40670.91350.445266°0.91350.40672.246025°0.42260.90630.466365°0.90630.42262.144526°0.43830.89870.487764°0.89870.43832.050327°0.45390.89100.509563°0.89100.

9、45391.962628°0.46940.88290.531762°0.88290.46941.880729°0.48480.87460.554361°0.87460.48481.804030°0.50000.86600.577360°0.86600.50001.732031°0.51500.85710.600859°0.85710.51501.664232°0.52990.84800.624858°0.84800.52991.600333°0.54460.83860.649457&#

10、176;0.83860.54461.539834°0.55910.82900.674556°0.82900.55911.482535°0.57350.81910.700255°0.81910.57351.428136°0.58770.80900.726554°0.80900.58771.376337°0.60180.79860.753553°0.79860.60181.327038°0.61560.78800.781252°0.78800.61561.279939°0.62930.77

11、710.809751°0.77710.62931.234840°0.64270.76600.839050°0.76600.64271.191741°0.65600.75470.869249°0.75470.65601.150342°0.66910.74310.900448°0.74310.66911.110643°0.68190.73130.932547°0.73130.68191.072344°0.69460.71930.965646°0.71930.69461.035545

12、6;0.70710.7071145°0.70710.70711同角基本關(guān)系式倒數(shù)關(guān)系商的關(guān)系平方關(guān)系tancot1sinsec22sincos1sincsc1tancsccos122cossec1coscsctansec22cotsecsin1cotcsc誘導(dǎo)公式sin()sincos()costan()tancot()cotsin()cossin()sin3cos()cossin(22cos()sintan()tan3cos(2cot()cot2tan()cottan(322cot()tancot( 322sin()cos2cos()sinsin()sinsin( 322cos()

13、costan()cotcos(3tan()tan22cot()tancot()cot3tan(223cot(兩角和與差的三角函數(shù)公式sin()sincoscossinsin()sincoscossincos()coscossinsincos()coscossinsintan()tantan1tantantan()tantan1tantan)cossin(2)sincos(2)cos)sintan(2)tancot(2)cot)cot(其中 k Z)tan)cossin(2)sin)sincos(2)costan(2)tan)cotcot(2)cot)tan萬能公式sin2 tan(/ 2)ta

14、n 2(/ 2)11tan 2(/ 2)costan 2(/ 2)1tan2 tan(/ 2)tan 2(/ 2)1半角的正弦、余弦和正切公式三角函數(shù)的降冪公式1cos21cos2sin()2sin22cos(1cos21cos2cos)222tan(1cos1 cossin)cossin1 cos21二倍角的正弦、余弦和正切公式三倍角的正弦、余弦和正切公式sin 22sincossin33sin4sin 3cos2cos2sin 22cos 21 1 2sin 2cos34cos33cos .tan 22 tantan33tantan313tan 21 tan 2三角函數(shù)的和差化積公式三角函數(shù)的積化和差公式sinsin2sincossincos1sin()sin()222sinsin2cossincossin1sin()sin()222coscos2coscoscoscos1cos()cos()222coscos2sinsinsinsin1cos