notes from trigonometry - s. butler

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1、NotesfromTrigonometryStevenButlerBrighamYoungUniversityFall2002ContentsPrefacevii1Theusefulnessofmathematics11.1WhatcanIlearnfrommath?.....................11.2Problemsolvingtechniques.......................21.3Theultimateinproblemsolving....................31.4Takeabreak....

2、..........................31.5Supplementalproblems.........................42Geometricfoundations52.1What’sspecialabouttriangles?....................52.2Somedefinitionsonangles.......................62.3Symbolsinmathematics........................72.4Isocelestriangles........

3、....................82.5Righttriangles.............................82.6Anglesumintriangles.........................92.7Supplementalproblems.........................103ThePythagoreantheorem133.1ThePythagoreantheorem.......................133.2ThePythagoreantheoremanddissectio

4、n...............143.3Scaling..................................153.4ThePythagoreantheoremandscaling................173.5Cavalieri’sprinciple...........................183.6ThePythagoreantheoremandCavalieri’sprinciple.........193.7Thebeginningofmeasurement.....................

5、193.8Supplementalproblems.........................214Anglemeasurement234.1Thewonderfulworldofπ........................234.2Circumferenceandareaofacircle...................24iCONTENTSii4.3Gradiansanddegrees..........................244.4Minutesandseconds......................

6、....264.5Radianmeasurement..........................264.6Convertingbetweenradiansanddegrees...............274.7Wonderfulworldofradians.......................284.8Supplementalproblems.........................285Trigonometrywithrighttriangles305.1Thetrigonometricfunctions.....

7、.................305.2Usingthetrigonometricfunctions...................325.3BasicIdentities.............................335.4ThePythagoreanidentities.......................335.5Trigonometricfunctionswithsomefamiliartriangles.........345.6Awordofwarning.......................

8、....355.7Supplementalproblems.........................356Trigonometrywithci