中二数学教学笔记第十一章三角比的认识

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1、中二數學教學筆記Chapter11IntroductiontoTrigonometricRatios(三角比的認識)數學新里程﹙第二版﹚SectionTopicTeachingNotesClassworkorHomework11.1三角比-Studentsshouldbeabletoidentifythenamesofhypotenuse,oppositesideandadjacentsideforaright-angledtriangle.11.2,4,6角的餘弦(cosine)-Studentsshouldbeabletotellthesideratioandt

2、hetrigonometricratios.角的正弦(sine)-Studentsshouldbeabletowritedownthetrigonometricequation.角的正切(tangent)-Studentsshouldbeabletousecalculatortofindtheangleanditstrigonometricratios.11.3,5,7餘弦函數的應用-Studentsshouldbeabletofindtheunknownsforproblems.正弦函數的應用-Studentsshouldbemakeusesinefunction

3、tofindtheareaoftrianglesand正切函數的應用parallelogram.11.8餘弦、正弦和正切三個三角-Studentsshouldbeabletoconstructtherequiredright-angledtriangle.Ex.11GQ.1-7函數的綜合應用1Rev.Ex.11Q.1-23-Studentsshouldbeabletousearea=absinθfortriangle,and2area=absinθforparallelogram-Studentsshouldbeabletofindtheareaofaregular

4、polygon.Supp.三角比的恆等式-Studentsshouldbeabletomakeusethetrigonometricidentitiesforcalculation:sinθtanθ=cosθ22sinθ+cosθ=1-Studentsshouldbeabletorecallthevaluesoftrigonometricfunctionsofspecialoooooanglessuchas0,30,45,60and90.-Studentsshouldbeabletosolveproblemsinvolvingcomplementaryangles.

5、SupplementaryExercise:三角比：測量實驗工作紙增潤資料：o1.簡介1度=60分，1分=60秒。符號方面：3度10分20秒可寫成310’20”2.應教授如何在計算機輸入度、分、秒方式表示的角度。3.簡介6個三角函數中、英名稱及其定義：中文名稱英文名稱函數定義對邊正弦函數sinefunctionsinθ=斜邊鄰邊餘弦函數cosinefunctioncosθ=斜邊對邊正切函數tangentfunctiontanθ=鄰邊鄰邊1餘切函數cotangentfunctioncotθ=cotθ=對邊tanθ斜邊1正割函數secantfunctionsecθ=se

6、cθ=鄰邊cosθ斜邊1餘割函數cosecantfunctioncscθ=cscθ=對邊sinθ4.簡介所有三角函數均是非線性函數(non-linearfunction)。5.利用計算機，計算角度的各個函數值、及由函數求角的大小。6.利用「單位圓」(unitcircle)介紹各函數與各線段長度的關係：cotθcscθ1tanθsinθθcosθsecθHarderexamples:1.Findtheareaofaregularhexagonofsidelength10cm.2.(a)Findtheareaofaregularpentagonofsidelength1

7、0cm.(b)Findtheareaofaregularoctagonofsidelength10cm.3.Comparetheareasofthefollowingfigures(allred-colouredandgreen-colouredlinesareofsamerespectivelylengths,andtheymakesameanglesinthefigures):diagonalsbisecteachotherdiagonalsdonotbisecteachothero4.Findtheareaofaquadrilateralwithdiago