高中数学公式大全

高中数学公式大全

高中数学公式大全，包括文科必背数学公式整理和重点数学公式大全。乘法与因式分：a^2-b^2=(a+b)(a-b)a^3+b^3=(a+b)(a^2-ab+b^2)a^3-b^3=(a-b)(a^2+ab+b^2)三角不等式：|a+b|≤|a|+|b||a-b|≤|a|+|b||a|≤b<=>-b≤a≤b|a-b|≥|a|-|b|-|a|≤a≤|a|一元二次方程的解：(-b+√(b^2-4ac))/2a(-b-√(b^2-4ac))/2a根与系数的关系：X1+X2=-b/aX1*X2=c/a注：韦达定理判别式：b^2-4ac=0注：方程有两个相等的实根b^2-4ac>0注：方程有两个不等的实根b^2-4ac<0注：方程没有实根，有共轭复数根三角函数公式：两角和公式：sin(A+B)=sinAcosB+cosAsinBsin(A-B)=sinAcosB-sinBcosAcos(A+B)=cosAcosB-sinAsinBcos(A-B)=cosAcosB+sinAsinBtan(A+B)=(tanA+tanB)/(1-tanAtanB)tan(A-B)=(tanA-tanB)/(1+tanAtanB)ctg(A+B)=(ctgActgB-1)/(ctgB+ctgA)ctg(A-B)=(ctgActgB+1)/(ctgB-ctgA)倍角公式：tan2A=2tanA/(1-tan^2A)ctg2A=(ctg^2A-1)/2ctgacos2a=cos^2a-sin^2a=2cos^2a-1=1-2sin^2a半角公式：sin(A/2)=√((1-cosA)/2)sin(A/2)=-√((1-cosA)/2)cos(A/2)=√((1+cosA)/2)cos(A/2)=-√((1+cosA)/2)tan(A/2)=√((1-cosA)/((1+cosA))tan(A/2)=-√((1-cosA)/((1+cosA))ctg(A/2)=√((1+cosA)/((1-cosA))ctg(A/2)=-√((1+cosA)/((1-cosA))和差化积：2sinAcosB=sin(A+B)+sin(A-B)2cosAsinB=sin(A+B)-sin(A-B)2cosAcosB=cos(A+B)-sin(A-B)-2sinAsinB=cos(A+B)-cos(A-B)sin(A+B)=2sin((A+B)/2)cos((A-B)/2)cos(A+B)=2cos((A+B)/2)sin((A-B)/2)tan(A+B)=sin(A+B)/(cosAcosB)tan(A-B)=sin(A-B)/(cosAcosB)ctg(A+B)=sin(A+B)/sinAsinBctg(A-B)=sin(A-B)/sinAsinB一些数列前n项和：1+2+3+4+5+6+7+8+9+...+n=n(n+1)/21+3+5+7+9+11+13+15+...+(2n-1)=n^22+4+6+8+10+12+14+...+2n=n(n+1)1^2+2^2+3^2+4^2+5^2+6^2+...+n^2=n(n+1)(2n+1)/61+2^2+3^2+4^2+5^2+6^2+...+n^2=n(n+1)(n+2)/3正弦定理：a/sinA=b/sinB=c/sinC=2R（其中R表示三角形的外接圆半径）余弦定理：b^2=a^2+c^2-2accosB（其中角B是边a和边c的夹角）圆的标准方程：(x-a)^2+(y-b)^2=r^2（其中(a,b)是圆心坐标）圆的一般方程：x^2+y^2+Dx+Ey+F=0（其中D^2+E^2-4F>0）抛物线标准方程：y^2=2px,y^2=-2px,x^2=2py,x^2=-2py直棱柱侧面积：S=c*h，斜棱柱侧面积：S=c'*h正棱锥侧面积：S=1/2c*h'，正棱台侧面积：S=1/2(c+c')h'圆台侧面积：S=1/2(c+c')l=pi(R+r)l，球的表面积：S=4pi*r^2圆柱侧面积：S=c*h=2pi*h，圆锥侧面积：S=1/2c*l=pi*r*l弧长公式：l=a*r（其中a是圆心角的弧度数，r>0）扇形面积公式：s=1/2*l*r锥体体积公式：V=1/3*S*H，圆锥体体积公式：V=1/3*pi*r^2h斜棱柱体积：V=S'L（其中S'是直截面面积，L是侧棱长）柱体体积公式：V=s*h，圆柱体体积：V=pi*r^2h高中文科数学必背公式总结：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，其中k为整数。cot(2kπ+α)=cotα，其中k为整数。对于任意角α，有π+α的三角函数值与α的三角函数值之间的关系：sin(π+α)=-sinαcos(π+α)=-cosαtan(π+α)=tanαcot(π+α)=cotα任意角α与其相反数-α的三角函数值之间的关系为：sin(-α)=-sinαcos(-α)=cosαtan(-α)=-tanαcot(-α)=-cotα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)=sinαcos(π-α)=-cosαtan(π-α)=-tanαcot(π-α)=-cotα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)=-sinαcos(2π-α)=cosαtan(2π-α)=-tanαcot(2π-α)=-cotα对于π/2±α及3π/2±α与α，它们的三角函数值之间的关系如下：sin(π/2+α)=cosαcos(π/2+α)=-sinαtan(π/2+α)=-cotαcot(π/2+α)=-tanαsin(π/2-α)=cosαcos(π/2-α)=sinαtan(π/2-α)=cotαcot(π/2-α)=tanαsin(3π/2+α)=-cosαcos(3π/2+α)=sinαtan(3π/2+α)=-cotαcot(3π/2+α)=-tanαsin(3π/2-α)=-cosαcos(3π/2-α)=-sinαtan(3π/2-α)=cotαcot(3π/2-α)=tanα（其中k为整数）两角和与差的三角函数公式如下：sin(α+β)=sinαcosβ+cosαsinβsin(α-β)=sinαcosβ-cosαsinβcos(α+β)=cosαcosβ-sinαsinβcos(α-β)=cosαcosβ+sinαsinβtan(α+β)=(tanα+tanβ)/(1-tanαtanβ)tan(α-β)=(tanα-tanβ)/(1+tanα·tanβ)二倍角的正弦、余弦和正切公式如下：sin2α=2sinαcosαCosinedoubleangleformula:cos2α=cos^2(α)-sin^2(α)=2cos^2(α)-1=1-2sin^2(α)Tangentdoubleangleformula:tan2α=2tanα/[1-tan^2(α)]Half-angleformulasforsine,cosine,andtangent:sin^2(α/2)=(1-cosα)/2cos^2(α/2)=(1+cosα)/2tan^2(α/2)=(1-cosα)/(1+cosα)Anotherformofthetangenthalf-angleformulaistan(α/2)=(1-cosα)/sinα=sinα/(1+cosα)Universalformulasforsine,cosine,andtangent: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)]Tripleangleformulasforsine,cosine,andtangent:sin3α=3sinα-4sin^3(α)cos3α=4cos^3(α)-3cosαtan3α=(3tanα-tan^3(α))/(1-3tan^2(α))Methodstoimprovehighschoolmathgrades:1.ActivepreviewingPreviewingistheprocessofactivelyacquiringnewknowledge,whichhelpstostimulatelearninginitiative.Beforethenewknowledgeisexplained,carefullyreadthetextbookandcultivatethehabitofactivelypreviewing,whichisanimportantwaytoacquiremathematicalknowledge.Therefore,payattentiontodevelopingself-learningabilityandlearntoreadbooks.Whenstudyingexampleproblems,understandthecontentoftheexample,theconditionsgiven,whatneedstobesolved,howthebooksolvestheproblem,whyitissolvedthisway,whethertherearenewmethods,andwhatthesolutionstepsare.Grasptheseimportantissues,thinkdeeply,andlearntouseexistingknowledgetoindependentlyexplorenewknowledge.2.ActivethinkingManystudentsonlylistenpassivelyduringclassanddonotactivelythink.Whenfacedwithrealproblems,theydonotknowhowtoapplywhattheyhavelearnedtosolvethem.Themainreasonisthelackofactivethinkingduringclass.Inadditiontofollowingtheteacher'sthinking,weshouldalsothinkmoreaboutwhythingsaredefinedthiswayandwhatthebenefitsareofsolvingproblemsthisway.Activethinkingnotonlyhelpsuslistenmorecarefullyinclassbutalsostimulatesinterestincertainknowledge,whichismoreconducivetolearning.Relyingontheteacher'sguidancetothinkabouttheproblem-solvingprocess;theanswerisnotreallyimportant;themethodis!3.GoodatsummarizingrulesSolvingmathproblemscangenerallyfollowcertainrules.Whensolvingproblems,payattentiontosummarizingtheproblem-solvingrules.Aftersolvingeachpracticeproblem,reviewthefollowingquestions:①Whatisthemostimportantcharacteristicofthisproblem?②Whatbasicknowledgeandbasicshapeswereusedtosolvethisproblem?③Howdidyouobserve,associate,andtransformtoachievethetransformation?4.在解决这道题目时，我们需要运用哪些数学思想和方法呢？5.在解决这道题目时，哪一步是最关键的呢？6.你是否曾经遇到过类似的题目？在解题方法和思路上有什么异同之处？7.你能够发现几种解题方法？哪一种方法最优？这种