三角函数特殊角值表

角度函数030456090120135150180270360角a的弧度0π/6π/4π/3π/22π/33π/45π/6π3π/22πsin01/2√2/2√3/21√3/2√2/21/20-10cos1√3/2√2/21/20-1/2-√2/2-√3/2-101tan0√3/31√3-√3-1-√3/3001、图示法：借助于下面三个图形来记忆，即使有所遗忘也可根据图形重新推出：sin30°=cos60°=21，sin45°=cos45°=22，tan30°=cot60°=33，tan45°=cot45°=1正弦函数sinθ=y/r余弦函数cosθ=x/r正切函数tanθ=y/x余切函数cotθ=x/y正割函数secθ=r/x余割函数cscθ=r/y2、列表法：说明：正弦值随角度变化，即0˚30˚45˚60˚90˚变化；值从02122231变化，其余类似记忆．3、规律记忆法：观察表中的数值特征，可总结为下列记忆规律：①有界性：（锐角三角函数值都是正值）即当0°＜＜90°时，则0＜sin＜1；0＜cos＜1；tan＞0；cot＞0。②增减性：（锐角的正弦、正切值随角度的增大而增大；余弦、余切值随角度的增大而减小），即当0＜A＜B＜90°时，则sinA＜sinB；tanA＜tanB；cosA＞cosB；cotA＞cotB；特别地：若0°＜＜45°，则sinA＜cosA；tanA＜cotA若45°＜A＜90°，则sinA＞cosA；tanA＞cotA．4、口决记忆法：观察表中的数值特征正弦、余弦值可表示为2m形式，正切、余切值可表示为3m形式，有关m的值可归纳成顺口溜：一、二、三；三、二、一；三九二十七．30˚123145˚121260˚3函数名正弦余弦正切余切正割余割符号sincostancotseccsc正弦函数sin（A）=a/c余弦函数cos（A）=b/c正切函数tan（A）=a/b余切函数cot（A）=b/a其中a为对边，b为邻边，c为斜边三角函数对照表三角函数SINCOSTAN三角函数SINCOSTAN0°01090°10无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°0.99750.069714.30065°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°0.17360.98480.176380°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°0.27560.96120.286774°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°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°0.89100.45391.962628°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°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°0.62930.77710.809751°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°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tancot1sincsc1cossec1sinsectancoscsccoscsccotsinsec222222sincos11tansec1cotcsc诱导公式sin()sincos()costan()tancot()cotsin()cos2cos()sin2tan()cot2cot()tan2sin()cos2cos()sin2tan()cot2cot()tan2sin()sincos()costan()tancot()cotsin()sincos()costan()tancot()cot3sin()cos23cos()sin23tan()cot23cot()tan23sin()cos23cos()sin23tan()cot23cot()tan2sin(2)sincos(2)costan(2)tancot(2)cot(其中k∈Z)sin(2)sincos(2)costan(2)tancot(2)cot两角和与差的三角函数公式万能公式sin()sincoscossinsin()sincoscossincos()coscossinsincos()coscossinsintantantan()1tantantantantan()1tantan2tan(/2)sin1tan2(/2)1tan2(/2)cos1tan2(/2)2tan(/2)tan1tan2(/2)半角的正弦、余弦和正切公式三角函数的降幂公式1cossin()221coscos()221cos1cossintan()21cossin1cos221cos2sin21cos2cos2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sin22sincoscos2cos2sin22cos2112sin22tantan21tan2sin33sin4sin3cos34cos33cos.3tantan3tan313tan2三角函数的和差化积公式三角函数的积化和差公式sinsin2sincos22sinsin2cossin22coscos2coscos22coscos2sinsin221sincossin()sin()21cossinsin()sin()21coscoscos()cos()21sinsincos()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tanba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。”