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TrigonometricRatiosInarightangledtriangle,thetrigonometricratiosforananglearedefinedasfollows:sinoppositeFindtheequationofLLineL2is perpendiculartoLbFindtheequationofLThesine,cosineandtangentratios.ThenotesandquestionsforSin,CosineRule&AreaofTrianglesUnitTheArea RuleSomebasicdefinitions–areminderStudythetriangleABCshownbelowTrigonometryisthestudyoflengthsandanglesintriangleshypotenuseAreaofa Triangle(SAS)InanytriangleABC,theareaAisgivenbythefollowingformulasAbcAsinAacBsinAabCsinExampleFindtheareaoftriangleABCifCq0cc SolutionBq0ccqq|q7nabABccaqqsinsinaqcqccmnB0cq|cmExampleFindtheareaoftriangleABCSolution1ThecosineruleThissectionlooksat trigonometryinright-angledtrianglesFind\(\hat{B}\)weusetheSineRulewhenwehaveoppositesFromtheGCSEformulasheetInanytriangleABCSine RulesinAsinBsinCCosineRulea: b'+c' 2bccosAreaoftriangle ahsinCweonlyeverusetwobitsofit!oppositeAlso,letb=AC,a=BCandc= AB.=BCAB.Ifatriangleisgivenwithtwosidesandtheincludedangleknown,thenwecannotsolvefortheremainingunknownsidesandanglesusingthesine rule.adjacentopposite.adjacent.Wethereforeinvestigatethecosinerule:In\(\triangleABC,AB=,AC=\)and\(\hat{A}=\text{33}\text{°}\).sin(B)sin(A) Whateverwewanttofindgoesontop,ifwewerefindingananglewewoulduse:sin(A)sin(B)(1,0)Usethearearuletocalculatetheareaof\(\triangleDEF\) In\(\triangleDEF\):\begin{align*}\text{Area}&=\frac{1}{2}d\timesh\\&=\frac{1}{2}df\sin\hat{E}1\endThisvideoprovesandappliestheArea Rulefornon-rightangledtrianglesThetrianglePQRisweusetheSineRulewhenwehaveoppositesFromtheGCSEformulasheetInanytriangleABCSine RulesinAsinBsinCCosineRulea: b'+c' 2bccosAreaofallowcorrectapplicationofcosineruleorfromfindingrelevantangleandusingtrigrottoormore sf,orB2fororbetterunsupportedAC2=oeAC=ThesineruleGradeCAPSUsingtheYouhavealreadymettheformulafortheareaofatrianglewhenthe lengthsoftwosidesandtheincludedangleareknown,ThusA=ab (cosC)=ab(1 cosC)((b)FindtheareaoftrianglePQR,clearlyindicatingtheunitsof youranswerContextualproblemsarewrittensothatlearnerscanhaveconceptualunderstandingC=DocumentDescription:Sin,CosineRule&Areaof TrianglesforYearispartofYearpreparationThediagramshowstrianglePQRcmcmcmDiagramnotdrawntoscaletancosMathematicsSeries hypotenuseadjacentLetBstandsfortheangleatBLetCstandfortheangleatCandsoon