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sinπii 3πiiiπWhatarethevaluesofiCalculatetheareaoftheequilateraltriangletan2ysin2y=sin2ycos2ysin2yconverttoallsinesandSolvetheequation overthesetofrealnumbers.Pluseachonecomeswithananswerkey.TrueorFalseThenumberofsolutionstotheequationsin2x sinx =intheinterval≤x≤ 2πisSolvetheproblem)Whatisthedomainofthecosinefunction?Calculatetheheight,x,oftheequilateraltriangleaboveSolvingThediagrambelowshows oneoftheequilateraltrianglesCalculatethePrecalculus:ProvingTrigonometricIdentitiesExampleProvethefollowingidentitytan2ysin2y=tan2ysin2yYou canusetrigonometricidentitiesyoualreadyknowtoprovenewidentities;MakesureyouknowthesimpletrigonometricidentitiesandWelcometothisshort ‘insightsvideo’showingsomeofthemisunderstandingslearnershavewhensolvingquestionswithtrigonometricquadratic,orcubic,equationsABCDhardlyever haveanythinglikeahintButthat’sOKbecausetheseproblemsareintendedastrainingproblemsπiiGivetheanswertothenearesthundredthThefirsttwo positiverootsoftheequationareandDeterminethegeneralProveidentitiesusingseveraltechniques.tan3πiv.cos3πiii.VerifyingTrigonometricIdentities.Lawof SinesandCosinesWorksheetQUESTIONIfsin°=aandcos°=b,determinethefollowingintermsofaand/orbcos28q(2)cos64q(3)sin4°(4)Provewithout theuseofacalculator,thatifsin°=aandcos°=b,thenbaab(4)Evaluateeachofthefollowingwithoutusingacalculatordefinitionsandpropertiesofthe trigonometricfunctionssin,cos,tan1)A)allrealnumbers,exceptintegralmultiplesof(°)B)allrealnumbersC)allrealnumbers,exceptoddmultiplesof(°)D)all realnumbersfromto1,inclusiveProveeachidentitysecx-tonxslnx=-secXseellsinlltane+cotesin'lIcos,ySin,Y='SinYsec'Oesc'sec'Identitiesworksheet name·,·eosxsinxesex+cotxseeOtanll cosOcotOese'Otan'II=tan'IItan'xsin'x=tan'xsin'xProvingIdentitiesProvesincotcosTTTProvetancossin(sec cot)xxxxxProvesincoosscTTTProvetancotseccscxxxxSumandDifferenceFormulasFindtheexactvalueforcos75qShowthatcos(2)cosxxSWrite cos3cos2sin3sin2xxxxasasinglecosineIfsinAwithAinQIand5Enjoythesefreesheets.sin7πVTrigonometryTestQuestionsForallx,sin(2x)=sinx.There areProvingtrigonometricidentities(1)GiveageometricprooffortheformulasforthesineandcosineofthesumoftwoanglesInthischapterwewilllookat morecomplexrelationshipsthatallowustoconsidercombiningandcomposingequationstrigonometricexpressionsandequationsThistestisincludedtohelp youcheckhowwellyouremembertheseExpressinradiansanglesofiiiiiiExpressindegreesanglesofiEachonehasmodelproblemsworkedoutstepbystep, practiceproblems,aswellaschallengequestionsatthesheetsendByTheprocessforshowingtwotrigonometricexpressionstobeequivalent(regardlessofthe valueoftheangle)isknownasvalidatingorprovingtrigonometricidentitiesNowthatyouarecomfortablesimplifyingexpressions,wewillextendtheideato verifyingentireTrigSectionGraphingtheTrigonometricFunctionsUnitCircleMULTIPLECHOICEπ√tan=TrueorFalseIfθisinthesecondquadrant,thenp1 sin2θ= cosθ.Alsotheyneveraskyoutoproveforyourselfsomemoreorlesswellknownresult,asmanyofthesequestionsdo.TrueorFalse.