初中三角函數(shù)知識(shí)點(diǎn)總結(jié)及中考真題講解學(xué)生版

初中三角函數(shù)知識(shí)點(diǎn)總結(jié)及中考真題講解學(xué)生版銳角三角函數(shù)知識(shí)點(diǎn)總結(jié)222b1、勾股定理:直角三角形兩直角邊、的平方和等于斜邊的平方。a，b,cac2、如下圖，在Rt?ABC中，?C為直角，則?A的銳角三角函數(shù)為(?A可換成?B):定義表達(dá)式取值范圍關(guān)系a，A的對(duì)邊0,sinA,1正sinA,cosBsinA,sinA,弦c(?A為銳角)斜邊cosA,sinB22b，A的鄰邊0,cosA,1余sinA，cosA,1cosA,cosA,c斜邊弦(?A為銳角)tanA,cotBa，A的對(duì)邊tanA,0正tanA,tanA,cotA,tanBb切(?A為銳角)，A的鄰邊1(倒數(shù))tanA,cotAbcotA,0，A的鄰邊余cotA,cotA,tanA,cotA,1a，A的對(duì)邊切(?A為銳角)3、任意銳角的正弦值等于它的余角的余弦值;任意銳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)對(duì)斜邊cosA,sin(90:,A)cosA,sinB得，B,90:,，Aca邊bAC鄰邊4、任意銳角的正切值等于它的余角的余切值;任意銳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?特殊角的三角函數(shù)值(重要)三角函數(shù)0?30?45?60?90?213sin,01222213cos,102223tan,301-33cot,3-1036、正弦、余弦的增減性:,,,,,當(dāng)0???90?時(shí)，sin隨的增大而增大，cos隨的增大而減小。7、正切、余切的增減性:,,,,,當(dāng)0?<<90?時(shí)，tan隨的增大而增大，cot隨的增大而減小。8、解直角三角形的定義:已知邊和角(兩個(gè)，其中必有一邊)?所有未知的邊和角。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依據(jù):?邊的關(guān)系:;?角的關(guān)系:A+B=90?;?邊角關(guān)系:三角函數(shù)的定義。(注意:盡量避a，b,c免使用中間數(shù)據(jù)和除法)9、應(yīng)用舉例:(1)仰角:視線在水平線上方的角;俯角:視線在水平線下方的角。視線鉛垂線水平線仰角ihl,:h俯角α視線lhhl1:mii,(2)坡面的鉛直高度和水平寬度的比叫做坡度(坡比)。用字母表示，即。坡度一般寫成的形式，li,1:5如等。h把坡面與水平面的夾角記作i,,tan,(叫做坡角)，那么。,l3、從某點(diǎn)的指北方向按順時(shí)針轉(zhuǎn)到目標(biāo)方向的水平角，叫做方位角。如圖3，OA、OB、OC、OD的方向角分別是:45?、135?、225?。4、指北或指南方向線與目標(biāo)方向線所成的小于90?的水平角，叫做方向角。如圖4,OA、OB、OC、OD的方向角分別是:北偏東30?(東北方向)，南偏東45?(東南方向)，南偏西60?(西南方向)，北偏西60?(西北方向)。tan,1.三角形在方格紙中的位置如圖所示，則的值是()3434A(B(C(D(534512.在?ABC中，?C,90?，tanA,，則sinB,()32310310A(B(C(D(3410103?O?ABC?O?OAC,2sinBAD3.如圖，是的外接圓，是的直徑，若的半徑為，，則的值是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，，則AB的長(zhǎng)是cm(58.如圖，角的頂點(diǎn)為O，它的一邊在x軸的正半軸上，另一邊OA上有一點(diǎn)P(3，4)，則,sin,,(329.如圖，菱形ABCD的邊長(zhǎng)為10cm，DE?AB，sinA,，則這個(gè)菱形的面積=cm(5三、解答題10.如圖是一個(gè)半圓形橋洞截面示意圖，圓心為O，直徑AB是河底線，弦CD是水位線，CD?AB，12且CD=24m，OE?CD于點(diǎn)E(已測(cè)得sin?DOE=(13EDCABO(1)求半徑OD;(2)根據(jù)需要，水面要以每小時(shí)0.5m的速度下降，則經(jīng)過多長(zhǎng)時(shí)間才能將水排干,ABCDBCAEBC,EDFAE,FDE11.如圖，在矩形中，是邊上的點(diǎn)，，，垂足為，連接(?ABE??DFA(1)求證:;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?蕪湖中考)如圖，在?ABC中，AD是BC上的高，，(1)求證:AC=BD;12sinC,(2)若，BC=12，求AD的長(zhǎng)(13要點(diǎn)二、特殊角的三角函數(shù)值1.的坐標(biāo)是()A(cos60?，,tan30?)關(guān)于原點(diǎn)對(duì)稱的點(diǎn)A1,,,,,,,,13331313A(B(C(D(,，,，,，,,，,,,,,,,,,,,,,,,,23222323,,,,,,,,二、填空題3,107.=______(:4cos30sin60(2)(20092008)::，,,,2三、解答題3,1011.計(jì)算:3+(2π,1),tan30?,tan45301,,200912.計(jì)算:(2sin603tan30(1)??,，，,,,3,,,,33sin602cos458,，13.)計(jì)算:1.某人想沿著梯子爬上高4米的房頂，梯子的傾斜角(梯子與地面的夾角)不能大于60?，否則就有危險(xiǎn)，那么梯子的長(zhǎng)至少為()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.如圖，在平地上種植樹木時(shí)，要求株距(相鄰兩樹間的水平距離)為4m(如果在坡度為0.75的山坡上種樹，也要求株距為4m，那么相鄰兩樹間的坡面距離為()A(5mB(6mC(7mD(8m，,BAD30?5.如圖，小明要測(cè)量河內(nèi)小島B到河邊公路l的距離，在A點(diǎn)測(cè)得，在C點(diǎn)測(cè)得，,BCD60?AC,50，又測(cè)得米，則小島到公路的距離為()米(Bl100325325253，A(25B(C(D(312.如圖(1)，一扇窗戶打開后用窗鉤AB可將其固定(如(2)是如圖(1)中窗子開到一定位置時(shí)的31.7?平面圖，若?AOB=45?，?OAB=30?，OA=60cm，求點(diǎn)B到OA邊的距離((，結(jié)果精確到整數(shù))13.如圖，數(shù)學(xué)活動(dòng)小組來到校園內(nèi)的一盞路燈下測(cè)量路燈的高度，測(cè)角儀AB的高度為1.5米，測(cè)得30?2,仰角為，點(diǎn)B到電燈桿底端N的距離BN為10米，求路燈的高度MN是多少米,(取=1.414，3=1.732，結(jié)果保留兩位小數(shù))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.如圖，某幼兒園為了加強(qiáng)安全管理，決定將園內(nèi)的滑滑板的傾角由45o降為30o，已知原滑滑板AB的長(zhǎng)為5米，點(diǎn)D、B、C在同一水平地面上((1)改善后滑滑板會(huì)加長(zhǎng)多少,(精確到0.01)(2)若滑滑板的正前方能有3米長(zhǎng)的空地就能保證安全，原滑滑板的前方有6米長(zhǎng)的空地，像這樣改造是否可行,說明理由。(參考數(shù)據(jù):)21.414,31.732,62.449,,,methanolmixedsolvent,insamplesofperoxideoxidationofferrousiron-xygendissolvedmethanehreeodependenttestresultsshallnotexceedthearithmeticalaverageofthe10%.Method2method1,principlesofspecimenwithttwosignificantfigures.5,precisionunderrepeatabilityconditionstoobtaintheabsolutevalueofthedifferenc