2014年高考数学一轮复习：高考常用的诱导公式汇总

2014年高考数学一轮复习：高考常用的诱导公式汇总 2014年高考数学一轮复习:高考常用的诱导公式汇总 一、高中数学诱导公式全集: 常用的诱导公式有以下几组: 公式一: 设α为任意角，终边相同的角的同一三角函数的值相等: sin(2kπ，α),sinα (k?Z) cos(2kπ，α),cosα (k?Z) tan(2kπ，α),tanα (k?Z) cot(2kπ，α),cotα (k?Z) 公式二: 设α为任意角，π+α的三角函数值与α的三角函数值之间的关系: sin(π，α),,sinα cos(π，α),,cosα tan(π，α),tanα cot(π，α),cotα 公式三: 任意角α与 -α的三角函数值之间的关系: sin(,α),,sinα cos(,α),cosα tan(,α),,tanα cot(,α),,cotα 公式四: 利用公式二和公式三可以得到π-α与α的三角函数值之间的关系: sin(π,α),sinα cos(π,α),,cosα tan(π,α),,tanα cot(π,α),,cotα 公式五: 利用公式一和公式三可以得到2π-α与α的三角函数值之间的关系: sin(2π,α),,sinα cos(2π,α),cosα tan(2π,α),,tanα cot(2π,α),,cotα 公式六: π/2?α及3π/2?α与α的三角函数值之间的关系: sin(π/2，α),cosα cos(π/2，α),,sinα tan(π/2，α),,cotα cot(π/2，α),,tanα sin(π/2,α),cosα cos(π/2,α),sinα tan(π/2,α),cotα cot(π/2,α),tanα procedure 6 SH3525-2004 petrochemical JB/ T4708-2000 of welding procedure qualification for steel pressure vessels 7 JB/4709-2000 8 JB4730-2005 pressure vessel welding procedures of steel pressure vessel NDT 9 JB/T4744-2000 steel pressure vessel products mechanical properties test of welded plate II, mechanical equipment installation engineering 1 GB150-98 2 GB50128-2005 vertical cylindrical steel pressure vessel steel welded tank code for construction and acceptance of 3 JB/ T4735-1997 steel welded atmospheric pressure vessel 4 GB50231-2009 mechanical equipment installation engineering construction and acceptance specification for 5 GB50275-98 compressor, fan and pump installation engineering construction and acceptance specification for lifting 6 HG20201-2000 construction installation engineering construction standard 7, HG ... Pressure gauges, using an installed spark arrestor for acetylene cylinders, illegal carrying, using gas cylinders, each operator fined 20 Yuan. Gas bottle without the hot sun exposure measures, responsibilities of team a fine of 50 Yuan. (7) at height and the opening and provisional protective measures have been taken, the responsible unit fined 200 Yuan, construction person in charge a fine of 50 Yuan. (8) no permit to work and the job in accordance with the provisions, on the job unit fined 300 yuan, the unit will charge a fine of 100 Yuan. 7.5.3 accident penalties (1) injuries fatalities directly punished 1~2 million. Direct responsibility for the accident and have the corresponding responsibility of leadership, such as concerning administrative sanctions, should be brought to the company or the relevant Department. (2) personal injury accident occurred, the direct punishment 0.5-10,000 yuan, responsible for the direct responsibility for the sin(3π/2，α),,cosα cos(3π/2，α),sinα tan(3π/2，α),,cotα cot(3π/2，α),,tanα sin(3π/2,α),,cosα cos(3π/2,α),,sinα π/2,α),cotα tan(3 cot(3π/2,α),tanα (以上k?Z) 注意:在做题时，将a看成锐角来做会比较好做。 诱导公式记忆口诀 ※规律 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 ※ 上面这些诱导公式可以概括为: 对于π/2*k ?α(k?Z)的三角函数值， ?当k是偶数时，得到α的同名函数值，即函数名不改变; ?当k是奇数时，得到α相应的余函数值，即sin?cos;cos?sin;tan?cot,cot?tan. (奇变偶不变) 然后在前面加上把α看成锐角时原函数值的符号。 (符号看象限) 例如: sin(2π,α),sin(4?π/2,α)，k,4为偶数，所以取sinα。 当α是锐角时，2π,α?(270?，360?)，sin(2π,α),0，符号为“,”。 所以sin(2π,α),,sinα 上述的记忆口诀是: 奇变偶不变，符号看象限。 公式右边的符号为把α视为锐角时，角k?360?+α(k?Z)，-α、180??α，360? -α 所在象限的原三角函数值的符号可记忆 水平诱导名不变;符号看象限。 , 各种三角函数在四个象限的符号如何判断，也可以记住口诀“一全正;二正弦(余割); 三两切;四余弦(正割)”( 这十二字口诀的意思就是说: 第一象限内任何一个角的四种三角函数值都是“，”; 第二象限内只有正弦是“，”，其余全部是“,”; 第三象限内切函数是“，”，弦函数是“,”; 第四象限内只有余弦是“，”，其余全部是“,”( 上述记忆口诀,一全正,二正弦,三内切,四余弦 , 还有一种按照函数类型分象限定正负: 函数类型 第一象限 第二象限 第三象限 第四象限 正弦 ...........，............，............—............—........ 余弦 ...........，............—............—............，........ 正切 ...........，............—............，............—........ procedure 6 SH3525-2004 petrochemical JB/ T4708-2000 of welding procedure qualification for steel pressure vessels 7 JB/4709-2000 8 JB4730-2005 pressure vessel welding procedures of steel pressure vessel NDT 9 JB/T4744-2000 steel pressure vessel products mechanical properties test of welded plate II, mechanical equipment installation engineering 1 GB150-98 2 GB50128-2005 vertical cylindrical steel pressure vessel steel welded tank code for construction and acceptance of 3 JB/ T4735-1997 steel welded atmospheric pressure vessel 4 GB50231-2009 mechanical equipment installation engineering construction and acceptance specification for 5 GB50275-98 compressor, fan and pump installation engineering construction and acceptance specification for lifting 6 HG20201-2000 construction installation engineering construction standard 7, HG ... Pressure gauges, using an installed spark arrestor for acetylene cylinders, illegal carrying, using gas cylinders, each operator fined 20 Yuan. Gas bottle without the hot sun exposure measures, responsibilities of team a fine of 50 Yuan. (7) at height and the opening and provisional protective measures have been taken, the responsible unit fined 200 Yuan, construction person in charge a fine of 50 Yuan. (8) no permit to work and the job in accordance with the provisions, on the job unit fined 300 yuan, the unit will charge a fine of 100 Yuan. 7.5.3 accident penalties (1) injuries fatalities directly punished 1~2 million. Direct responsibility for the accident and have the corresponding responsibility of leadership, such as concerning administrative sanctions, should be brought to the company or the relevant Department. (2) personal injury accident occurred, the direct punishment 0.5-10,000 yuan, responsible for the direct responsibility for the 余切 ...........，............—............，............—........ 同角三角函数基本关系 同角三角函数的基本关系式 倒数关系: tanα ?cotα,1 sinα ?cscα,1 1 cosα ?secα, 商的关系: sinα/cosα,tanα,secα/cscα cosα/sinα,cotα,cscα/secα 平方关系: sin^2(α)，cos^2(α),1 1，tan^2(α),sec^2(α) 1，cot^2(α),csc^2(α) 同角三角函数关系六角形记忆法 六角形记忆法:(参看图片或参考资料链接) 构造以"上弦、中切、下割;左正、右余、中间1"的正六边形为模型。 (1)倒数关系:对角线上两个函数互为倒数; (2)商数关系:六边形任意一顶点上的函数值等于与它相邻的两个顶点上函数值的乘 积。 (主要是两条虚线两端的三角函数值的乘积)。由此，可得商数关系式。 (3)平方关系:在带有阴影线的三角形中，上面两个顶点上的三角函数值的平方和等 于下面顶点上的三角函数值的平方。 两角和差公式 两角和与差的三角函数公式 sin(α，β),sinαcosβ，cosαsinβ sin(α,β),sinαcosβ,cosαsinβ cos(α，β),cosαcosβ,sinαsinβ cos(α,β),cosαcosβ，sinαsinβ tan(α，β),(tanα+tanβ),(1-tanαtanβ) tan(α,β),(tanα,tanβ),(1，tanα?tanβ) 二倍角公式 二倍角的正弦、余弦和正切公式(升幂缩角公式) sin2α,2sinαcosα cos2α,cos^2(α),sin^2(α),2cos^2(α),1,1,2sin^2(α) tan2α,2tanα/[1,tan^2(α)] 半角公式 半角的正弦、余弦和正切公式(降幂扩角公式) sin^2(α/2),(1,cosα),2 cos^2(α/2),(1，cosα),2 tan^2(α/2),(1,cosα),(1，cosα) 另也有tan(α/2)=(1,cosα)/sinα=sinα/(1+cosα) 万能公式 万能公式 procedure 6 SH3525-2004 petrochemical JB/ T4708-2000 of welding procedure qualification for steel pressure vessels 7 JB/4709-2000 8 JB4730-2005 pressure vessel welding procedures of steel pressure vessel NDT 9 JB/T4744-2000 steel pressure vessel products mechanical properties test of welded plate II, mechanical equipment installation engineering 1 GB150-98 2 GB50128-2005 vertical cylindrical steel pressure vessel steel welded tank code for construction and acceptance of 3 JB/ T4735-1997 steel welded atmospheric pressure vessel 4 GB50231-2009 mechanical equipment installation engineering construction and acceptance specification for 5 GB50275-98 compressor, fan and pump installation engineering construction and acceptance specification for lifting 6 HG20201-2000 construction installation engineering construction standard 7, HG ... Pressure gauges, using an installed spark arrestor for acetylene cylinders, illegal carrying, using gas cylinders, each operator fined 20 Yuan. Gas bottle without the hot sun exposure measures, responsibilities of team a fine of 50 Yuan. (7) at height and the opening and provisional protective measures have been taken, the responsible unit fined 200 Yuan, construction person in charge a fine of 50 Yuan. (8) no permit to work and the job in accordance with the provisions, on the job unit fined 300 yuan, the unit will charge a fine of 100 Yuan. 7.5.3 accident penalties (1) injuries fatalities directly punished 1~2 million. Direct responsibility for the accident and have the corresponding responsibility of leadership, such as concerning administrative sanctions, should be brought to the company or the relevant Department. (2) personal injury accident occurred, the direct punishment 0.5-10,000 yuan, responsible for the direct responsibility for the sinα=2tan(α/2)/[1+tan^2(α/2)] cosα=[1-tan^2(α/2)]/[1+tan^2(α/2)] tanα=2tan(α/2)/[1-tan^2(α/2)] 万能公式推导 附推导: sin2α=2sinαcosα=2sinαcosα/(cos^2(α)+sin^2(α))......*， (因为cos^2(α)+sin^2(α)=1) 再把*分式上下同除cos^2(α)，可得sin2α,2tanα/(1，tan^2(α)) 然后用α/2代替α即可。 同理可推导余弦的万能公式。正切的万能公式可通过正弦比余弦得到。 三倍角公式 三倍角的正弦、余弦和正切公式 sin3α,3sinα,4sin^3(α) cos3α,4cos^3(α),3cosα tan3α,[3tanα,tan^3(α)],[1,3tan^2(α)] 三倍角公式推导 附推导: tan3α,sin3α/cos3α ,(sin2αcosα，cos2αsinα)/(cos2αcosα-sin2αsinα) ,(2sinαcos^2(α)，cos^2(α)sinα,sin^3(α))/(cos^3(α),cosαsin^2(α), 2sin^2(α)cosα) 上下同除以cos^3(α)，得: tan3α,(3tanα,tan^3(α))/(1-3tan^2(α)) sin3α,sin(2α，α),sin2αcosα，cos2αsinα ,2sinαcos^2(α)，(1,2sin^2(α))sinα ,2sinα,2sin^3(α)，sinα,2sin^3(α) ,3sinα,4sin^3(α) cos3α,cos(2α，α),cos2αcosα,sin2αsinα ,(2cos^2(α),1)cosα,2cosαsin^2(α) ,2cos^3(α),cosα，(2cosα,2cos^3(α)) ,4cos^3(α),3cosα 即 sin3α,3sinα,4sin^3(α) cos3α,4cos^3(α),3cosα 三倍角公式联想记忆 ?记忆方法:谐音、联想 正弦三倍角:3元 减 4元3角(欠债了(被减成负数)，所以要“挣钱”(音似“正弦”)) 余弦三倍角:4元3角 减 3元(减完之后还有“余”) ??注意函数名，即正弦的三倍角都用正弦 表 关于同志近三年现实表现材料材料类招标技术评分表图表与交易pdf视力表打印pdf用图表说话 pdf 示，余弦的三倍角都用余弦表示。 ?另外的记忆方法: 正弦三倍角: 山无司令 (谐音为 三无四立) 三指的是"3倍"sinα, 无指的是减号, 四指 的是"4倍", 立指的是sinα立方 余弦三倍角: 司令无山 与上同理 和差化积公式 procedure 6 SH3525-2004 petrochemical JB/ T4708-2000 of welding procedure qualification for steel pressure vessels 7 JB/4709-2000 8 JB4730-2005 pressure vessel welding procedures of steel pressure vessel NDT 9 JB/T4744-2000 steel pressure vessel products mechanical properties test of welded plate II, mechanical equipment installation engineering 1 GB150-98 2 GB50128-2005 vertical cylindrical steel pressure vessel steel welded tank code for construction and acceptance of 3 JB/ T4735-1997 steel welded atmospheric pressure vessel 4 GB50231-2009 mechanical equipment installation engineering construction and acceptance specification for 5 GB50275-98 compressor, fan and pump installation engineering construction and acceptance specification for lifting 6 HG20201-2000 construction installation engineering construction standard 7, HG ... Pressure gauges, using an installed spark arrestor for acetylene cylinders, illegal carrying, using gas cylinders, each operator fined 20 Yuan. Gas bottle without the hot sun exposure measures, responsibilities of team a fine of 50 Yuan. (7) at height and the opening and provisional protective measures have been taken, the responsible unit fined 200 Yuan, construction person in charge a fine of 50 Yuan. (8) no permit to work and the job in accordance with the provisions, on the job unit fined 300 yuan, the unit will charge a fine of 100 Yuan. 7.5.3 accident penalties (1) injuries fatalities directly punished 1~2 million. Direct responsibility for the accident and have the corresponding responsibility of leadership, such as concerning administrative sanctions, should be brought to the company or the relevant Department. (2) personal injury accident occurred, the direct punishment 0.5-10,000 yuan, responsible for the direct responsibility for the 三角函数的和差化积公式 sinα，sinβ,2sin[(α，β)/2]?cos[(α,β)/2] sinα,sinβ,2cos[(α，β)/2]?sin[(α,β)/2] cosα，cosβ,2cos[(α，β)/2]?cos[(α,β)/2] cosα,cosβ,,2sin[(α，β)/2]?sin[(α,β)/2] 积化和差公式 三角函数的积化和差公式 sinα ?cosβ,0.5[sin(α，β)，sin(α,β)] cosα ?sinβ,0.5[sin(α，β),sin(α,β)] cosα ?cosβ,0.5[cos(α，β)，cos(α,β)] sinα ?sinβ,,0.5[cos(α，β),cos(α,β)] 和差化积公式推导 附推导: 首先,我们知道sin(a+b)=sina*cosb+cosa*sinb,sin(a-b)=sina*cosb-cosa*sinb 我们把两式相加就得到sin(a+b)+sin(a-b)=2sina*cosb 所以,sina*cosb=(sin(a+b)+sin(a-b))/2 同理,若把两式相减,就得到cosa*sinb=(sin(a+b)-sin(a-b))/2 同样的,我们还知道cos(a+b)=cosa*cosb-sina*sinb,cos(a-b)=cosa*cosb+sina*sinb 所以,把两式相加,我们就可以得到cos(a+b)+cos(a-b)=2cosa*cosb 所以我们就得到,cosa*cosb=(cos(a+b)+cos(a-b))/2 同理,两式相减我们就得到sina*sinb=-(cos(a+b)-cos(a-b))/2 这样,我们就得到了积化和差的四个公式: sina*cosb=(sin(a+b)+sin(a-b))/2 cosa*sinb=(sin(a+b)-sin(a-b))/2 cosa*cosb=(cos(a+b)+cos(a-b))/2 sina*sinb=-(cos(a+b)-cos(a-b))/2 好,有了积化和差的四个公式以后,我们只需一个变形,就可以得到和差化积的四个公式. 我们把上述四个公式中的a+b设为x,a-b设为y,那么a=(x+y)/2,b=(x-y)/2 把a,b分别用x,y表示就可以得到和差化积的四个公式: sinx+siny=2sin((x+y)/2)*cos((x-y)/2) sinx-siny=2cos((x+y)/2)*sin((x-y)/2) cosx+cosy=2cos((x+y)/2)*cos((x-y)/2) cosx-cosy=-2sin((x+y)/2)*sin((x-y)/2) procedure 6 SH3525-2004 petrochemical JB/ T4708-2000 of welding procedure qualification for steel pressure vessels 7 JB/4709-2000 8 JB4730-2005 pressure vessel welding procedures of steel pressure vessel NDT 9 JB/T4744-2000 steel pressure vessel products mechanical properties test of welded plate II, mechanical equipment installation engineering 1 GB150-98 2 GB50128-2005 vertical cylindrical steel pressure vessel steel welded tank code for construction and acceptance of 3 JB/ T4735-1997 steel welded atmospheric pressure vessel 4 GB50231-2009 mechanical equipment installation engineering construction and acceptance specification for 5 GB50275-98 compressor, fan and pump installation engineering construction and acceptance specification for lifting 6 HG20201-2000 construction installation engineering construction standard 7, HG ... Pressure gauges, using an installed spark arrestor for acetylene cylinders, illegal carrying, using gas cylinders, each operator fined 20 Yuan. Gas bottle without the hot sun exposure measures, responsibilities of team a fine of 50 Yuan. (7) at height and the opening and provisional protective measures have been taken, the responsible unit fined 200 Yuan, construction person in charge a fine of 50 Yuan. (8) no permit to work and the job in accordance with the provisions, on the job unit fined 300 yuan, the unit will charge a fine of 100 Yuan. 7.5.3 accident penalties (1) injuries fatalities directly punished 1~2 million. Direct responsibility for the accident and have the corresponding responsibility of leadership, such as concerning administrative sanctions, should be brought to the company or the relevant Department. (2) personal injury accident occurred, the direct punishment 0.5-10,000 yuan, responsible for the direct responsibility for the