Algebra and Trigonometry

1178 Pages·2007·68.98 MB·English

by  Michael Sullivan

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Preftaotc heIe n structor xiii
liosfAt p plications xix
PhoCtroe dits xxv
Tot hSet udent xxvii
Review
R 1
R.1R eaNlu mbers 2
R.2A lgeEbssrean tials 17
R.3G eomeEtssreyn tials 30
R.4P olynomials 39
R.SF actoring Polynomials 49
R.6S yhnettiDci vision 57
R.7R aitonEaxlp ressions 61
R.8n tRho oRtast;i Eoxnpaoln ents 72
ChaptReerv iew 80
ChapteTres t 84
1 EquatioannsdI nequalities 85
1.1Li nEeaqura tions 86
1.2Q uardaitEcq uations 97
1.3C ompNluemxb ;eQ ruasdraEtquiact iiontneh s
CompNluemxb er System 109
14. RadiEcqauilao ;tnE squatiQouandsr aitnF iorcm ;
FactorEaqubaltei ons 118
1.5S ovlignI nequalities 124
1.6E quatioInnse qaunIadnl vviotiglAin bess oVlauultee 135
17. PorblSeomln gvI:in tteM,ri exstUunirfeo,Mr omt ion,
anCdo nsRtaatnJebtoA pplications 139
ChaptReerv iew 148
ChaptTeerst 152
ChaptPerro jects 153
2 Graphs 155
2.1T heD istaannMdci ed pFooirnmtu las 156
2.2G rhapso fE quatiiTnow onV sar ia;bI lnetserScyempmtest;r y1 63
2.3L ines 173
2.4C ircles 189
2.5V ariation 195
vii
viiiCo ntents
ChaptReerv iew 201
ChaptTeerst 204
CumulatiRveev iew 204
ChaptPerro ject 205
FunctioannsdT heiGrr aphs
3 207
3.1F unctions 208
ThGer aho pfaF unicnot 222
3.2
3.3P orperotfFi uensc tions 231
3.4L ibroafFr uyn cntsPi;ei oecwise-Fduenfcitnieodn s 242
3.5G raphTeicnhqgnu i:eT sranosrfmations 252
3.6M athemMaotdiecBlausli: l Fduinncgt ions 264
ChaptReerv iew 269
ChaptTeers t 274
CumulatiRveev iew 275
ChaptPerro jects 276
4 Lineaarn dQ uadratFiucn ctions 277
4.1L inFeuanrc tainTodhne siP ror perties 278
4.2B uildLiinngFe uanrc tfirooDnmas t a 287
4.3Q uadraFutnticico annTsdh ePiorrp erties 293
4.4Q uadrMaotdliesBc;u ilQduidanrgaF tuincc tfirooDnmas t a 305
4.5I nequIanlviotlQivueiasnd grF autnicct ions 314
ChaptReerv iew 318
ChapteTres t 320
Cumulatei Rveview 321
ChaptPerro jects 322
. - -
PolynomainadlR ationFauln ctions
5 323
51. PolynFoumnicatlai noMdno sd els 324
52. PropeorfRt aiteisFo unnaclt ions 344
53. ThGer aopfhR aat iFounnaclt ion 355
5.4P olynaonmRdia atli Ionneaqlu alities 369
5.5T hRee aZler soo faP olynFoumnicatli on 375
5.6C ompZleerxoFs u;n damTehnetoaorlefA ml gebra 389
ChaptReerv iew 394
ChaptTeerst 398
CumulatiRveev iew 398
ChaptPerro jects 399
Contentsi x
G ExponentainadlL ogarithFmuincc tions 401
6.1C ompoFsuintcet ions 402
6.2O net--oOneF uncntsIi;no veFrusnec tions 409
6.3E xponenFtuinaclt ions 423
6.4L ogariFtuhnmcitci ons 437
6.5P orperotfLi oegsa rithms 450
6.6L ogariatnEhdxm pioc neEnqutaitailo ns 459
6.7C ompoIunntde rest 465
6.8E xponenGtrioawaltn hDd e cMaoyd lesN;e wtoLna'ws;
LogiGsrtoiwct hD eacMnadoy d els 475
6.9B uilEdxipnogn eLnotgiaarlia,tn hLdmo igciM,so tdiecl s
from Data 487
ChaptReerv iew 494
ChaptTeers t 500
CumulatiRveev iew 501
ChaptPerro jects 502
7 TrigonomeFturnicct ions 503
7.1A ngleTsh eaMinerda sure 504
7.2R igThrita nTgrilgeo nometry 517
7.3C omputthiVenal gu oefTsri gonomFeutnrcitocifA o cnusAt neg le52s9
7.4T rigonomFeutnrcitocifG o ennseA rnagll es 540
7.5U niCtir Acplper oPaorcphe;ro tfti heTesri gonomFeutnrcitci o55n0s
7.6G rapohfs S tihaneen C do siFnuen ctions 560
7.7G rapohfs T tanhgee Cnott,a nCgoesnetca,an Sndet c,Fa unntc ti57o4n s
7.8P hsaeS hiSfitn;u lsC ouviredF aitting 581
ChaptReerv iew 592
ChaptTeers t 598
CumulatiRveev iew 598
Chapter Projects 599
8 AnalytTirci gonometry 601
8.1T hIen veSrisnCeeo ,s iannTedan, g eFnutn ctions 602
8.2T hIen veTrrisgeo nomFeutnrcit(cioC onntsi nued) 614
8.3Tr igonomIedternitci ties 620
8.4S uma nDdfi freenFcoer mulas 627
8.5D ouble-aannHdga llef -Faornmgullea s 637
8.6P ordu-cot-tSmu anSdu m-to-FPorrmoudluacst 646
8.7T rgionomEeqturaitc(i Io)n s 649
8.8T rigonomEeqturait(ciI oIn)s 656
ChaptReerv iew 663
ChaptTeerst 666
CumulatiRveev iew 667
ChaptPerro jects 667
X Contents
ApplicatoifoT nrsi gonomeFturnicct ions
9 669
9.1A pplicIavntloiivnoRgni sgT hrti angles 670
9.2T hLea wo fS ines 675
9.3T he LaCwos oifne s 686
9.4A reoafa T riangle 691
9.5S impHlarem oMnoiotcniD ;a mpMeodot niC;o mbiWnaievnsg 697
ChaptReerv iew 707
ChaptTeers t 710
Cumulatei Rveview 711
ChaptPerro jects 711
PolaCro ordinates; Vectors
10 713
10.P1ol Caoro rdinates 714
10.P2o lEaqura tiaonGndrs a phs 722
10.T3h Ceo mpPlleax;Dn eeMoivTrhee'osr em 738
10.V4e ctors 746
10.T5hD eo Ptr oduct 757
ChaptReerv iew 765
ChapteTres t 768
CumulatiRveev iew 769
ChaptePrr ojects 769
11 AnalytGieco metry 771
11.Co1n ics 772
1.12T hPera abola 773
1.13T hEel lipse 782
114 T.hHey perbola 792
1.15R otaotfAi xo;enG s eneFroarlom fa C onic 804
11.6P olEaqura tioofCn osn ics 812
1.17P alnCeu rvaenPsdra ameEtquraitci ons 818
ChaptReerv iew 830
ChaptTeers t 833
CumulatiRveev iew 833
ChaptPerro jects 834
12 SystemosfE quatioannsdI nequalities 835
12.S1y stoefLm isn Eeqauria o:tnS substiatnEudlt iimoinn atio83n6
12.S2y stoefLm isn Eeqaura :tM iaotnrsices 850
12.S3y stoefLm isn Eeqaura ntsDi:eo terminants 865
1.24M atArligxe bra 875
12.P5ra tFiaraclt Dieocno mipoons it 891