(ebook) [math] Trigonometry

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1、MathsExtension1–TrigonometryTrigonometryØTrigonometricRatiosØExactValues&TrianglesØTrigonometricIdentitiesØASTCRuleØTrigonometricGraphsØSine&CosineRulesØAreaofaTriangleØTrigonometricEquationsØSumsandDifferencesofanglesØDoubleAnglesØTripleAnglesØHalfAnglesØT–formulaØSubsidiary

2、AngleformulaØGeneralSolutionsofTrigonometricEquationsØRadiansØArcs,Sectors,SegmentsØTrigonometricLimitsØDifferentiationofTrigonometricFunctionsØIntegrationofTrigonometricFunctionsØIntegrationofsin2xandcos2xØINVERSETRIGNOMETRYØInverseSin–Graph,Domain,Range,PropertiesØInverseCo

3、s–Graph,Domain,Range,PropertiesØInverseTan–Graph,Domain,Range,PropertiesØDifferentiationofInverseTrigonometricFunctionsØIntegrationofInverseTrigonometricFunctionshttp://fatmuscle.cjb.net23MathsExtension1–TrigonometryTrigonometricRatiosoppositeadjacentadjacentoppositehypotenus

4、ehypotenuseθθSinesin=Cosinecos=Tangenttan=Cosecantcosec==Secantsec==Cotangentcot==sin=cos=tan=cosec=sec=cot=60seconds=1minute60’’=1’60minutes=1degree60’=1°http://fatmuscle.cjb.net23MathsExtension1–TrigonometryExactValues&Triangles1230°60°1145°0°30°60°45°90°180°01010–101––0ec–

5、–21––12–––1––10––TrigonometricIdentities=1===cosec2=cosec2–11=cosec2–==1=http://fatmuscle.cjb.net23MathsExtension1–TrigonometryASTCRule90°180°270°SATC1stQuadrant4thQuadrant2ndQuadrant3rdQuadrantFirstQuadrant:Allpositive+++SecondQuadrant:Sinepositive+––––ThirdQuadrant:Tangentp

6、ositive––––+FourthQuadrant:Cosinepositive––+––http://fatmuscle.cjb.net23MathsExtension1–TrigonometryTrigonometricGraphsSine&CosineRulesSineRule:ORABCCosineRule:Ahttp://fatmuscle.cjb.net23MathsExtension1–TrigonometryAreaofaTriangleØCistheangleØ&arethetwoadjacentsidesChttp://fa

7、tmuscle.cjb.net23MathsExtension1–TrigonometryTrigonometricEquationsØCheckthedomaineg.ØCheckdegrees()orradians()ØIfdoubleangle,go2revolutionsØIftripleangle,go3revolutions,etc…ØIfhalfangles,gohalforonerevolution(safeside)Example1Solvesinθ=for==30°,150°Example2Solvecos2θ=for==60

8、°,300°,420°,660°=30°,150°,210°,330°Example3Solvetan=1fortan=1=45°,22