初中三角函数知识点总结及中考真题讲解学生版

初中三角函数知识点总结及中考真题讲解学生版锐角三角函数知识点总结222b1、勾股定理:直角三角形两直角边、的平方和等于斜边的平方。a，b,cac2、如下图，在Rt?ABC中，?C为直角，则?A的锐角三角函数为(?A可换成?B):定义表达式取值范围关系a，A的对边0,sinA,1正sinA,cosBsinA,sinA,弦c(?A为锐角)斜边cosA,sinB22b，A的邻边0,cosA,1余sinA，cosA,1cosA,cosA,c斜边弦(?A为锐角)tanA,cotBa，A的对边tanA,0正tanA,tanA,cotA,tanBb切(?A为锐角)，A的邻边1(倒数)tanA,cotAbcotA,0，A的邻边余cotA,cotA,tanA,cotA,1a，A的对边切(?A为锐角)3、任意锐角的正弦值等于它的余角的余弦值;任意锐角的余弦值等于它的余角的正弦值。B由，A，，B,90:sinA,cosBsinA,cos(90:,A)对斜边cosA,sin(90:,A)cosA,sinB得，B,90:,，Aca边bAC邻边4、任意锐角的正切值等于它的余角的余切值;任意锐角的余切值等于它的余角的正切值。tanA,cotB由，A，，B,90:tanA,cot(90:,A)cotA,tanBcotA,tan(90:,A)得，B,90:,，A5、0?、30?、45?、60?、90?特殊角的三角函数值(重要)三角函数0?30?45?60?90?213sin,01222213cos,102223tan,301-33cot,3-1036、正弦、余弦的增减性:,,,,,当0???90?时，sin随的增大而增大，cos随的增大而减小。7、正切、余切的增减性:,,,,,当0?<<90?时，tan随的增大而增大，cot随的增大而减小。8、解直角三角形的定义:已知边和角(两个，其中必有一边)?所有未知的边和角。applytheediblepartsofthespecimenshatteredafterplacedinaflask,add30?-60?petroleumether100mL,shock1minovernight,filterbyfunnelcontaininganhydroussodiumsulfate,vacuumsolventrecoveryoronawaterbathat60?,petroleumether,forstand-by.Determinationofextractionofoilshouldmeetthefollowingrequirements.Weigh2.00g-3.00gmethodtoextracttheoilasdescribedabove,putiniodine250mLbottle,add30mLofchloroform-aceticmixture,sothatthespecimeniscompletelydissolved.Addl.00mLofsaturatedpotassiumiodidesolution,tightlystuffedbottlesaX2--theperoxidevalueofthesample,expressedinmeq/kg(MEQ/kg);V1--consumptionofsodiumthiosulfatestandardfrozenreduced-sizedropsofthesample,expressedinmilliliters(mL);V2--volumeofconsumedreagentblanktitrationwithsodiumthiosulfatestandardsolution.Milliliters(mL);Ca-titrationwithsodiumthiosulfatestandardsolutionconcentration,measuredinmolesperliter(mol/l);M--qualityofthesample,expressedingrams(g);0.1269-1.00mLtitrationwithsodiumthiosulfatestandardsolutionwas[c(Na2S2O3)=1.000mol/L]thequalityofiodineinunitsofgrams(g);78.8--conversionfactors.Resultstotwosignificantfigures.5,precisionunderrepeatabilityconditionstoobtaintheabsolutevalueofthedifferenceoftwoindependenttestresultsshallnotexceedthearithmeticalaverageofthe10%.Method2method1,principlesofspecimenwiththreeoxygendissolvedmethane-methanolmixedsolvent,insamplesofperoxideoxidationofferrousiron222依据:?边的关系:;?角的关系:A+B=90?;?边角关系:三角函数的定义。(注意:尽量避a，b,c免使用中间数据和除法)9、应用举例:(1)仰角:视线在水平线上方的角;俯角:视线在水平线下方的角。视线铅垂线水平线仰角ihl,:h俯角α视线lhhl1:mii,(2)坡面的铅直高度和水平宽度的比叫做坡度(坡比)。用字母表示，即。坡度一般写成的形式，li,1:5如等。h把坡面与水平面的夹角记作i,,tan,(叫做坡角)，那么。,l3、从某点的指北方向按顺时针转到目标方向的水平角，叫做方位角。如图3，OA、OB、OC、OD的方向角分别是:45?、135?、225?。4、指北或指南方向线与目标方向线所成的小于90?的水平角，叫做方向角。如图4,OA、OB、OC、OD的方向角分别是:北偏东30?(东北方向)，南偏东45?(东南方向)，南偏西60?(西南方向)，北偏西60?(西北方向)。tan,1.三角形在方格纸中的位置如图所示，则的值是()3434A(B(C(D(534512.在?ABC中，?C,90?，tanA,，则sinB,()32310310A(B(C(D(3410103?O?ABC?O?OAC,2sinBAD3.如图，是的外接圆，是的直径，若的半径为，，则的值是2()methanolmixedsolvent,insamplesofperoxideoxidationofferrousiron-xygendissolvedmethanehreeodependenttestresultsshallnotexceedthearithmeticalaverageofthe10%.Method2method1,principlesofspecimenwithttwosignificantfigures.5,precisionunderrepeatabilityconditionstoobtaintheabsolutevalueofthedifferenceoftwoinconversionfactors.Resultsto--ams(g);78.81.00mLtitrationwithsodiumthiosulfatestandardsolutionwas[c(Na2S2O3)=1.000mol/L]thequalityofiodineinunitsofgr-qualityofthesample,expressedingrams(g);0.1269--molesperliter(mol/l);Mtitrationwithsodiumthiosulfatestandardsolutionconcentration,measuredin-volumeofconsumedreagentblanktitrationwithsodiumthiosulfatestandardsolution.Milliliters(mL);Ca--sizedropsofthesample,expressedinmilliliters(mL);V2-cedconsumptionofsodiumthiosulfatestandardfrozenredu--theperoxidevalueofthesample,expressedinmeq/kg(MEQ/kg);V1--lesaX2xture,sothatthespecimeniscompletelydissolved.Addl.00mLofsaturatedpotassiumiodidesolution,tightlystuffedbottaceticmi-3.00gmethodtoextracttheoilasdescribedabove,putiniodine250mLbottle,add30mLofchloroform-by.Determinationofextractionofoilshouldmeetthefollowingrequirements.Weigh2.00g-,petroleumether,forstand?nawaterbathat60eryoropetroleumether100mL,shock1minovernight,filterbyfunnelcontaininganhydroussodiumsulfate,vacuumsolventrecov?60-?applytheediblepartsofthespecimenshatteredafterplacedinaflask,add3022334A(B(C(D(32433sinA,7.在?ABC中，?C,90?，BC,6cm，，则AB的长是cm(58.如图，角的顶点为O，它的一边在x轴的正半轴上，另一边OA上有一点P(3，4)，则,sin,,(329.如图，菱形ABCD的边长为10cm，DE?AB，sinA,，则这个菱形的面积=cm(5三、解答题10.如图是一个半圆形桥洞截面示意图，圆心为O，直径AB是河底线，弦CD是水位线，CD?AB，12且CD=24m，OE?CD于点E(已测得sin?DOE=(13EDCABO(1)求半径OD;(2)根据需要，水面要以每小时0.5m的速度下降，则经过多长时间才能将水排干,ABCDBCAEBC,EDFAE,FDE11.如图，在矩形中，是边上的点，，，垂足为，连接(?ABE??DFA(1)求证:;methanolmixedsolvent,insamplesofperoxideoxidationofferrousiron-alaverageofthe10%.Method2method1,principlesofspecimenwiththreeoxygendissolvedmethanelueofthedifferenceoftwoindependenttestresultsshallnotexceedthearithmeticconversionfactors.Resultstotwosignificantfigures.5,precisionunderrepeatabilityconditionstoobtaintheabsoluteva--alityofiodineinunitsofgrams(g);78.81.00mLtitrationwithsodiumthiosulfatestandardsolutionwas[c(Na2S2O3)=1.000mol/L]thequ-qualityofthesample,expressedingrams(g);0.1269--trationwithsodiumthiosulfatestandardsolutionconcentration,measuredinmolesperliter(mol/l);Mti-volumeofconsumedreagentblanktitrationwithsodiumthiosulfatestandardsolution.Milliliters(mL);Ca--sizedropsofthesample,expressedinmilliliters(mL);V2-consumptionofsodiumthiosulfatestandardfrozenreduced--nmeq/kg(MEQ/kg);V1theperoxidevalueofthesample,expressedi--ffedbottlesaX2aceticmixture,sothatthespecimeniscompletelydissolved.Addl.00mLofsaturatedpotassiumiodidesolution,tightlystu-escribedabove,putiniodine250mLbottle,add30mLofchloroform3.00gmethodtoextracttheoilasd-by.Determinationofextractionofoilshouldmeetthefollowingrequirements.Weigh2.00g-nd,petroleumether,forsta?rbyfunnelcontaininganhydroussodiumsulfate,vacuumsolventrecoveryoronawaterbathat60petroleumether100mL,shock1minovernight,filte?60-?applytheediblepartsofthespecimenshatteredafterplacedinaflask,add303(2)如果ADAB,10，=6，求sin，EDF的值(ADFBCEtancosBDAC,，14.(2007?芜湖中考)如图，在?ABC中，AD是BC上的高，，(1)求证:AC=BD;12sinC,(2)若，BC=12，求AD的长(13要点二、特殊角的三角函数值1.的坐标是()A(cos60?，,tan30?)关于原点对称的点A1,,,,,,,,13331313A(B(C(D(,，,，,，,,，,,,,,,,,,,,,,,,,23222323,,,,,,,,二、填空题3,107.=______(:4cos30sin60(2)(20092008)::，,,,2三、解答题3,1011.计算:3+(2π,1),tan30?,tan45301,,200912.计算:(2sin603tan30(1)??,，，,,,3,,,,33sin602cos458,，13.)计算:1.某人想沿着梯子爬上高4米的房顶，梯子的倾斜角(梯子与地面的夹角)不能大于60?，否则就有危险，那么梯子的长至少为()methanolmixedsolvent,insamplesofperoxideoxidationofferrousiron-xygendissolvedmethanehreeodependenttestresultsshallnotexceedthearithmeticalaverageofthe10%.Method2method1,principlesofspecimenwithttwosignificantfigures.5,precisionunderrepeatabilityconditionstoobtaintheabsolutevalueofthedifferenceoftwoinconversionfactors.Resultsto--ams(g);78.81.00mLtitrationwithsodiumthiosulfatestandardsolutionwas[c(Na2S2O3)=1.000mol/L]thequalityofiodineinunitsofgr-qualityofthesample,expressedingrams(g);0.1269--molesperliter(mol/l);Mtitrationwithsodiumthiosulfatestandardsolutionconcentration,measuredin-volumeofconsumedreagentblanktitrationwithsodiumthiosulfatestandardsolution.Milliliters(mL);Ca--sizedropsofthesample,expressedinmilliliters(mL);V2-cedconsumptionofsodiumthiosulfatestandardfrozenredu--theperoxidevalueofthesample,expressedinmeq/kg(MEQ/kg);V1--lesaX2xture,sothatthespecimeniscompletelydissolved.Addl.00mLofsaturatedpotassiumiodidesolution,tightlystuffedbottaceticmi-3.00gmethodtoextracttheoilasdescribedabove,putiniodine250mLbottle,add30mLofchloroform-by.Determinationofextractionofoilshouldmeetthefollowingrequirements.Weigh2.00g-,petroleumether,forstand?nawaterbathat60eryoropetroleumether100mL,shock1minovernight,filterbyfunnelcontaininganhydroussodiumsulfate,vacuumsolventrecov?60-?applytheediblepartsofthespecimenshatteredafterplacedinaflask,add3044383A(8米B(米C(米D(米83334.如图，在平地上种植树木时，要求株距(相邻两树间的水平距离)为4m(如果在坡度为0.75的山坡上种树，也要求株距为4m，那么相邻两树间的坡面距离为()A(5mB(6mC(7mD(8m，,BAD30?5.如图，小明要测量河内小岛B到河边公路l的距离，在A点测得，在C点测得，,BCD60?AC,50，又测得米，则小岛到公路的距离为()米(Bl100325325253，A(25B(C(D(312.如图(1)，一扇窗户打开后用窗钩AB可将其固定(如(2)是如图(1)中窗子开到一定位置时的31.7?平面图，若?AOB=45?，?OAB=30?，OA=60cm，求点B到OA边的距离((，结果精确到整数)13.如图，数学活动小组来到校园内的一盏路灯下测量路灯的高度，测角仪AB的高度为1.5米，测得30?2,仰角为，点B到电灯杆底端N的距离BN为10米，求路灯的高度MN是多少米,(取=1.414，3=1.732，结果保留两位小数)methanolmixedsolvent,insamplesofperoxideoxidationofferrousiron-alaverageofthe10%.Method2method1,principlesofspecimenwiththreeoxygendissolvedmethanelueofthedifferenceoftwoindependenttestresultsshallnotexceedthearithmeticconversionfactors.Resultstotwosignificantfigures.5,precisionunderrepeatabilityconditionstoobtaintheabsoluteva--alityofiodineinunitsofgrams(g);78.81.00mLtitrationwithsodiumthiosulfatestandardsolutionwas[c(Na2S2O3)=1.000mol/L]thequ-qualityofthesample,expressedingrams(g);0.1269--trationwithsodiumthiosulfatestandardsolutionconcentration,measuredinmolesperliter(mol/l);Mti-volumeofconsumedreagentblanktitrationwithsodiumthiosulfatestandardsolution.Milliliters(mL);Ca--sizedropsofthesample,expressedinmilliliters(mL);V2-consumptionofsodiumthiosulfatestandardfrozenreduced--nmeq/kg(MEQ/kg);V1theperoxidevalueofthesample,expressedi--ffedbottlesaX2aceticmixture,sothatthespecimeniscompletelydissolved.Addl.00mLofsaturatedpotassiumiodidesolution,tightlystu-escribedabove,putiniodine250mLbottle,add30mLofchloroform3.00gmethodtoextracttheoilasd-by.Determinationofextractionofoilshouldmeetthefollowingrequirements.Weigh2.00g-nd,petroleumether,forsta?rbyfunnelcontaininganhydroussodiumsulfate,vacuumsolventrecoveryoronawaterbathat60petroleumether100mL,shock1minovernight,filte?60-?applytheediblepartsofthespecimenshatteredafterplacedinaflask,add30516.如图，某幼儿园为了加强安全管理，决定将园内的滑滑板的倾角由45º降为30º，已知原滑滑板AB的长为5米，点D、B、C在同一水平地面上((1)改善后滑滑板会加长多少,(精确到0.01)(2)若滑滑板的正前方能有3米长的空地就能保证安全，原滑滑板的前方有6米长的空地，像这样改造是否可行,说明理由。(参考数据:)21.414,31.732,62.449,,,methanolmixedsolvent,insamplesofperoxideoxidationofferrousiron-xygendissolvedmethanehreeodependenttestresultsshallnotexceedthearithmeticalaverageofthe10%.Method2method1,principlesofspecimenwithttwosignificantfigures.5,precisionunderrepeatabilityconditionstoobtaintheabsolutevalueofthedifferenc