版三角函数特殊角值表格

精品文档精品文档PAGEPAGE5精品文档PAGE角度030456090120135150180270360函数角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°°=1，sin45°=cos45°=2，tan30°=cot60°=3，tan45°=cot45°=122322123130?45?60?311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0123变化，其余类似记忆．2223、规律记忆法：观察表中的数值特征，可 总结 初级经济法重点总结下载党员个人总结TXt高中句型全总结.doc高中句型全总结.doc理论力学知识点总结pdf 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m形式，正切、余切值可表示为m形式，有关m的值可归纳成23顺口溜：一、二、三；三、二、一；三九二十七．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tancot1sinsec22sincos1sincsc1tancsccos122cossec1coscsctansec22cotsecsin1cotcsc诱导公式sin()sincos()costan()tancot()cotsin()cossin()sin3cos()cossin(22cos()sintan()tan3cos(2cot()cot2tan()cottan(322cot()tancot(322sin()cos2cos()sinsin()sinsin(322cos()costan()cotcos(3tan()tan22cot()tancot()cot3tan(223cot(两角和与差的三角函数公式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万能公式sin2tan(/2)tan2(/2)11tan2(/2)costan2(/2)1tan2tan(/2)tan2(/2)1半角的正弦、余弦和正切公式三角函数的降幂公式1cos21cos2sin()2sin22cos(1cos21cos2cos)222tan(1cos1cossin)cossin1cos21二倍角的正弦、余弦和正切公式三倍角的正弦、余弦和正切公式sin22sincossin33sin4sin3cos2cos2sin22cos2112sin2cos34cos33cos.tan22tantan33tantan313tan21tan2三角函数的和差化积公式三角函数的积化和差公式sinsin2sincossincos1sin()sin()222sinsin2cossincossin1sin()sin()222coscos2coscoscoscos1cos()cos()222coscos2sinsinsinsin1cos()cos()222化asinα±bcos为α一个角的一个三角函数的形式（辅助角的三角函数的公式）asinxbcosxa2b2sin(x)ba、b的符号确定，tan其中角所在的象限由角的值由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。”