[A._Panchishkin,_E._Shavgulidze]_Trigonometric_Functions (1)

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1、,.)"Ji.',""".,"/TRIGONOMETRICFUNCTIONSlIIs,A.A.I1aHlJRmKlIH,E.T.llIaBryJIR)J,3eTPl1rOHOMETPI1QECRI1E

2、tedfromRussianI;byLeonidLevantt/1Firstpublished1988IRevisedfromthe1986RussianeditionrIHaanaAuiic1:0MnsunePrintedintheUnionofSovietSocialistRepublicsISBN5-03-000222-7©1I3p;aTeJIhcTBo«HayKa.,I'aaanaapenasnaa.pHaHKO-MaTeMaTHQeCKOiinareparypu,1986©Englishtransla

3、tion,MirPublishers,1988FroD1theJuthorsBytradition,trigonometryisanimportantcomponentofmathematicscoursesathighschool,andtrigonometryquestionsarealwayssetatoralandwrittenexamina•tionstothoseenteringuniversities,engineeringcolleges,andteacher-traininginstitut

4、es.Theaimofthisstudyaidistohelpthestudenttomas•terthebasictechniquesofsolvingdifficultproblemsintrigonometryusingappropriatedefinitionsandtheoremsfromtheschoolcourseofmathematics.Topresentthematerialinasmoothway,wehaveenrichedthetextwithsometheoreticalmateri

5、alfromthetextbookAlgebraandFundamentalsofAnalysiseditedbyAcademicianA.N.KolmogorovandanexperimentaltextbookofthesametitlebyProfessorsN.Ya.Vilenkin,A.G.Mordko•vich,andV.K.Smyshlyaev,focussingourattentionontheapplicationoftheorytosolutionofproblems.Thatiswhyou

6、rbookcontainsmanyworkedcompetitionproblemsandalsosomeproblemstobesolvedindepend•ently(theyaregivenattheendofeachchapter,theanswersbeingattheendofthebook).SomeofthegeneralmaterialistakenfromElementaryMathematicsbyProfessorsG.V.Dorofeev,M.K.Potapov,andN.Kh.Roz

7、ov(MirPublishers,Moscow,1982),whichisoneofthebeststudyaidsonmathematicsforpre•collegestudents.Weshouldliketonoteherethatgeometricalproblemswhichcanbesolvedtrigonometricallyandproblemsinvolvingintegralswithtrigonometricfunctionsarenotconsidered.Atpresent,ther

8、eareseveralproblemhooksonmathe•matics(trigonometryincluded)forthosepreparingtopasstheirentranceexaminations(forinstance,Problems6FromtheAuthorsatEntranceExaminationsinMathematicsbyYu.V.Nes•teren