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Department
Mathematics
Course
Mathematics 1225A/B
Professor
Vicki Olds
Semester
Winter

Description
Math1225ABUnit3TrigonometricFunctionstextreferenceSections62and64customtextpgs5676cVOlds2012Unit3333TrigonometricFunctionsInthischapterourmainfocusisondoingCalculuswithTrigonometricFunctionswhichisintextsection64TheCalculusitselfisquitestraightforwardTherewillbeasmallnumberofnewspecicderivativestoremembertwowouldsucebutitwillprobablybeeasiertomemorizeafewothersaswellButtherearentanynewdierentiationrulesjustthesameoldrulesappliedtonewkindsoffunctionsSotheresreallynotmuchthatsnewhereinthewayofCalculusHoweveritiscertainlyworthwhiledoingsomereviewofwhatTrigonometricFunctionsareandhowtheyworkAswelltheunitsinwhichwemeasureanglesinCalculusmaybenewtoyouAllthereviewyoureallyneeduscoveredinsection62andthesenotesbutyoumayalsonditusefultolookattextsection61andyoushouldcertainlydotheassignedhomeworkexercisesfromsection62whichreviewsthethingsyouneedtoknowabouttrigfunctionsbeforeworkingontheTrigDerivativescoveredinsection64PerhapsthemostimportantthingforyoutogetoutofthereviewwedoissomethingthatsoundssobasicitshouldntbeaproblemTrigfunctionsarefunctionsWellofcoursetheyareObviouslytheyareItsayssorightthereinthenametrigfunctionsHoweverforgettingthatornotunderstandingitintherstplaceseemstobethebiggestproblemthatstudentshaveinthissectionofthematerialBecausewithfunctionscomecompositefunctionsThatisifweapplyafunctiontoanythingmorecomplicatedthanxortorwhateverthevariablemayhappentobecalledthenwhatwehaveisacompositefunctionAndwhenyoudoCalculuswithacompositefunctionthenyouneedtheChainRuleWithtrigfunctionsjustlikewithexponentialandlogarithmicfunctionstheresalwayslotsofChainRuleneededKeepinginmindthatthesetrigfunctionsarefunctionswillhelpyoutorecognizewhenthoserulesareneededPerhapsagoodplacetostartisreviewingwhatwemeanbyafunctiontohelpyouseethatthesenewfunctionsweregoingtobeworkingwitharefunctionsBecauseinpreviouscourseswhenyouvedonetrigonometryyouwerentreallythinkingofthesefunctionsasfunctionsSoletsstartbyrecallingwhatafunctionisDenition31AfunctionfisarulethatassignstoeachelementofthedomainexactlyonevaluefromtherangeThatisforeachvaluexinthedomainofffassociatestheuniquevaluefxwiththevaluexAndofcoursethevariablemightnotbecalledxItcouldbetoryorororwhateverFornoparticularreasonwetendtousetasthevariablealotofthetimewithtrigfunctionsNowsometrigfunctionsYouprobablyrecallthatthereareanumberofthemSixinfactButtherearetwomaintrigfunctionsandthenalltheothersaredenedintermsofthosetwoSowestartwiththemDenition32ForanyangletthasauniquesinevaluedenotedsintandalsoauniquecosinevaluedenotedcostThatisthereisasinefunctiondenotedftsintwhosedomainisthesetofallanglesandwhichassociatesaparticularvaluewiththeangletAhaMaybethatstheproblemMaybethereasonthatsomestudentshavedicultyrealizingthatthisisafunctionisbecausewedontnecessarilyusethebracketsWenormallywritefunctionsasftorgtbutthenwewritethesinefunctionassintnotsintIfthatsgoingtocauseyouaproblemjustimaginethatsinisalwaysfollowedbyinvisiblebracketsGettingbacktowhatweweresayingthissinefunctionisarulethatassociateswitheverynumberangletinitsdomainauniquevaluewhichwecallsintSothatsafunctionSimilarlythereisanotherfunctionthecosinefunctiondenotedgtcost
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