三角函数的诱导公式练习题一.选择题1.下列各式不正确的是()A.sin(α+180°)=-sinαB.cos(-α+β)=-cos(α-β)C.sin(-α-360°)=-sinαD.cos(-α-β)=cos(α+β)2.600sin的值为()A.21B.21C.23D.233.619sin的值等于()A.21B.21C.23D.234.sin585°的值为()A.-22B.22C.-32D.325.sin(-236π)的值是()A.12B.-12C.32D.-326.cos(-225°)+sin(-225°)等于()A.22B.-22C.0D.27.cos2010°=()A.-12B.-32C.12D.328.已知sin(α-π4)=13,则cos(π4+α)的值为()A.223B.-223C.13D.-139.若,2,53cos则2sin的值是()A.53B.53C.54D.5410.已知cos(3π2+α)=-35,且α是第四象限角,则cos(-3π+α)()A.45B.-45C.±45D.3511.sin34·cos625·tan45的值是()A.-43B.43C.-43D.4312.若1sin()2,则cos的值为()A.12;B.12;C.32;D.3213.已知cos(π2+φ)=32,且|φ|<π2,则tanφ=()A.-33B.33C.-3D.314.设tan(5π+α)=m,则sinα-3π+cosπ-αsin-α-cosπ+α的值等于()A.m+1m-1B.m-1m+1C.-1D.115.A、B、C为△ABC的三个内角,下列关系式中不成立的是()①cos(A+B)=cosC②cosB+C2=sinA2③tan(A+B)=-tanC④sin(2A+B+C)=sinAA.①②B.③④C.①④D.②③16.已知3sin()42,则3sin()4值为()A.21B.—21C.23D.—2317.cos(+α)=—21,23π<α<2,sin(2-α)值为()A.23B.21C.23D.—2318.tan110°=k,则sin70°的值为()AA.-k1+k2B.k1+k2C.1+k2kD.-1+k2k19.化简:)2cos()2sin(21?得()A.sin2cos2B.cos2sin2C.sin2cos2D.±cos2sin220.已知3tan,23,那么sincos的值是()A231B231C231D23121.(2011年潍坊高一检测)已知a=tan(-7π6),b=cos234π,c=sin(-334π),则a、b、c的大小关系是()A.b>a>cB.a>b>cC.b>c>aD.a>c>b22.(2009.济南高一检测)若sincos2sincos,则3sin()sin()2-5等于()A.34B.310C.310D.31023.(2009·福州高一检测)已知f(cosx)=cos3x,则f(sin30°)的值等于()(A)-1(B)1(C)12(D)0二.填空题1、tan2010°的值为.2.sin(-317π)=.3.tan7π4-cos(-7π3)+sin(-13π6)的值为________.4.cos(-x)=23,x∈(-,),则x的值为.5.化简1-2sin200°cos160°=________.cos20°-sin20°6.若P(-4,3)是角α终边上一点,则cos(α-3π)·tan(α-2π)sin2(π-α)的值为________.7.式子cos2π4-α+cos2π4+α=________.18.若tan(π-α)=2,则2sin(3π+α)·cos5π2+α+sin32π-α·sin(π-α)的值为________.9.化简:)(cos)5sin()4sin()3(sin)(cos)4cos(222=_________.10.已知29cossin4cossin3,则tan=.11.若atan,则3cos5sin=________.12.如果,0sintan且,1cossin0那么的终边在第象限13.求值:2sin(-1110o)-sin960o+)210cos()225cos(2=.14.已知cos(π6+θ)=33,则cos(11π6-θ)=________.15.已知,41cos则23sin16,已知0cos100m,则0tan80的值是三.解答题1、求cos(-2640°)+sin1665°的值.2.化简(1)sin()cos()tan(2)(2)0sin(180)cos()tan()3.已知4sin()5,且sincos0,求2sin()3tan(3)4cos(3)的值4.化简sin(5)cos()cos(8)23sin()sin(4)25.已知f(α)=cosπ2+α·cos2π-α·sin-α+3π2sin-π-α·sin3π2+α.(1)化简f(α);(2)若α是第三象限角,且cos(α-3π2)=15,求f(α)的值.6.设()f)cos()7(cos221)cos(2)(sincos2223,求()3f的值.7.已知方程sin(3)=2cos(4),求)sin()23sin(2)2cos(5)sin(的值。8.若sinα,cosα是关于x的方程3x2+6mx+2m+1=0的两根,求实数m的值.9.求证:)π5sin()πcos()π6cos()π2sin()π2tan(=tanθ.10.已知2sin()cos()3()2,求下列各式的值:(1)sincos(2)33sin()cos()22三角函数的诱导公式练习题——参考答案一.题号123456789101112答案BDAAACBDCBAD题号131415161718192021222324答案CACCAACBABA二.1.33;2.23;3.-2;4.56π;5.cos20°-sin20°;6.-53;7.1;8.2;9.cos10.51;11.21aa;12....