precalculus_a problems-oriented approach_6th_2004_0534402127

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1、RESULTSFROMGEOMETRYTriangleCircleArea1bhAreaπr2r2hCircumference2πrbTrapezoidaParallelogramAreah(ab)hAreabhh2bbRectangularBoxSphere43rVolumelwhhlVolume3πrSurfacearea4πr2Surfacearea2wh2lh2wlwRightCircularCylinderRightCircularConeVolumeπr2hhVolume1πr2hh3Lat

2、eralsurfacearea2πrhrLateralsurfaceareaπrœ„„„„„„r2h2r•Thesumoftheanglesinatriangleis180°.THEOREMSFORPROVINGTHATTWOTRIANGLESARECONGRUENT:•Twosidesofatriangleareequalifandonlyiftheanglesoppositethosesidesareequal.1.Iftwosidesandtheincludedangleofonetriangleareequalres

3、pectivelytotwosidesandtheincludedangle•Ina30°-60°righttriangle,thelengthofthesideofanothertriangle,thenthetrianglesarecongruent.oppositethe30°angleishalfthelengthofthehypotenuse.2.Iftwoanglesandtheincludedsideofonetriangleareequalrespectivelytotwoanglesandtheincludeds

4、ideTHEPYTHAGOREANTHEOREM:Inarighttriangle,ofanothertriangle,thenthetrianglesarecongruent.thesquareofthelengthofthehypotenuseequalsthesum3.Ifthethreesidesofonetriangleareequalrespectivelyofthesquaresofthelengthsoftheothertwosides.tothethreesidesofanothertriangle,thenth

5、etrianglesarecongruent.HERON’SFORMULA:Ifa,b,andcarethelengthsofthesidesofatriangle,thentheareaofthetriangleisTHEOREMSFORPROVINGTHATTWOTRIANGLESARESIMILAR:1s1sa21sb21sc21.Iftwoanglesofonetriangleareequalrespectivelytowheretwoanglesofanothertriangle,thenthetrianglesa

6、re1similar.s21abc22.Ifthecorrespondingsidesoftwotrianglesarepropor-tional,thenthetrianglesaresimilar.GRAPHSyyyslopemr(x, y)11(h, k)xxxaay-y=m(x-x)(x-h)2+(y-k)2=r22211y=œ„„„„„„a-xyyyxxxy=

7、x

8、y=x2y=x3yyyxxx1y=œx„y=xy=[x]yxy=eyy(0, b)y=ln x(0, 1)b(_a, 0)(a, 0)xxx(1, 0

9、)ax2y2x2y2y=´andy=ln xa2+b2=1a2-b2=1Tiredofwaitingforofficehours?Takechargeofyourlearning…withiLrn™Tutorial!YoucanbeginusingiLrnTutorialrightaway!Justlogonusingtheaccesscodeboundinthistext.You’llfindtext-specific,self-pacedtutorialsthatofferexplanations,examples,step-

10、by-stepproblem-solvinghelp,andunlimitedpractice.You’llalsohaveaccesstochapter-by-chaptervideolessonsandliveonlinetutorialhel