DOCUMENT RESUME ED 053 927 SE 011 332 AUTHOR Brant, Vincent TITLE Trigonometry, A Tentative Guide Prepared for Use with the Text Plane Trigonometry with Tables. INSTITUTION Baltimore County Public Schools, Towson, Md. PUB DATE 65 NOTE 99p. AVAILABLE FROM Baltimore County Public Schools, Office of Curriculum Development, Towson, Maryland 21204 ($2.00) EDRS PRICE EDRS Price MF-$0.65 HC-$3.29 DESCRIPTORS Curriculum, *Curriculum Guides, Instruction, Mathematics, *Secondary School Mathematics, *Teaching Guides, *Trigonometry ABSTRACT This teacher's guide for a semester course in trigonometry is prepared for use with the text "Plane Trigonometry with Tables" by E. R. Heineman. Included is a daily schedule of topics for discussion and homework assignments. The scope of each lesson and teaching suggestions are provided. The content for the course includes trigonometric functions, solution of right triangles, trigonometric equations and identities, oblique triangles, and inverse trigonometric functions. Also included are two supplementary units on special right triangles and set theory. (Author/CT) U.S. DEPARTMENT OF HEALTH. EDUCATION & WELFARE OFFICE OF EDUCATION THIS DOCUMENT HAS BEEN REPRO. DUCED EXACTLY AS RECEIVED FROM THE PERSON OR ORGANIZATION ORIG . INATING IT POINTS OF VIEW OR OPIN IONS STATED DO NOT NECESSARILY REPRESENT OFFICIAL OFFICE OF EDU CATION POSITION OR POLICY CURRICULUM GUIDE TRIGONOMETRY A Tentative Guide Prepared for Use with the Text Plane Trigonometry with Tables by E. R. Heineman Guide Produced by Vincent Brant Supervisor of Senior High School Mathematics William S. Sartorius, Superintendent Tow son, Maryland 1965 2 BOARD OF EDUCATION OF BALTIMORE COUNTY Aigbu.rth Manor Towson, Maryland 21204 T. Bayard Williams, Jr. President Mrs. John M. Crocker H. Ems lie Parks Vice-President Mrs. Robert L. Berney Ramsay B. Thomas, M. D. H. Russell Knust Richard W. Tracey, D. V. M. William S. Sartorius Secretary-Treasurer and Superintendent of Schools Foreword This tentative guide has been written to aid teachers in presenting an updated course in trigonometry.The function concept as a set of ordered pairs and the analytic approach are key features of this guide. The lessons as well as the homework assignments are given as sug- gestions.The teacher should feel free to modify the lesson structure as may be appropriate for the student in his class.This guide serves as a framework within which the teacher should base the course in trigonometry.If teachers desire to alter the course to a considerable degree, they should discuss this with their department chairman or supervisor.Since this guide is tentative and will be revised after being used in the classroom, teachers are encouraged to offer suggestions and criticisms which will strengthen the outline. Teachers should not overlook the excellent transparency pro- jectuals which are in each mathematics department.Visual and graphic means should be used whenever possible. 4 MATERIALS OF THE COURSE IN TRIGONOMETRY Plane Trigonometry with Tables by E. R. Heineman will be used as the basic text. The references to the right of the scope in the outline indicate helpful or additional materials for the teacher and pupils. Code Title of Reference RWM Rosenbach, Whitman, Moskowitz.Plane Trigonometry with Tables. New York: Ginn and Company. 1943 FSM Fr eilich, Shanholt, McCormack. Plane Trigonometry. Morristown, N. J.:Silver Burdett Company. 1957. B Brant, Vincent.Relations, Functions, and Graphs. Towson, Maryland: Board of Education of Baltimore County.1962. AK Aiken and Beseman. Modern Mathematics:Topics and Problems.(Teacher's Edition). New York: McGraw- Hill Book Company. BW Butler and Wren. Trigonometry for Secondary Schools. Boston:D. C. Heath and Company. 1948. M May, K. 0.Elements of Modern Mathematics. Reading, Massachusetts: Addison-Wesley Publishing Company. 1959. Br Brady Transparency Projectuals 5 CONTENTS UNIT ONE THE TRIGONOMETRIC FUNCTIONS 1 UNIT TWO - SOLUTION OF RIGHT TRIANGLES .. 32 UNIT THREE - LINE REPRESENTATION OF TRIGONOMETRIC FUNCTION VALUES 36 UNIT FOUR SIMPLE IDENTITIES AND EQUATIONS 0 52 UNIT FIVE FUNCTIONS OF TWO ANGLES 59 UNIT SIX TRIGONOMETRIC EQUATIONS 63 UNIT SEVEN LOGARITHMS 64 UNIT EIGHT LOGARITHMIC SOLUTION OF RIGHT TRIANGLES 67 UNIT NINE OBLIQUE TRIANGLES 68 UNIT TEN INVERSE TRIGONOMETRIC FUNCTIONS . 75 UNIT ELEVEN- COMPLEX NUMBERS 78 APPENDIX I- SPECIAL RIGHT TRIANGLES APPENDIX II- REVIEW OF ELEMENTARY SET CONCEPTS LESSON SCOPEThe AND Trigonometric TEACHINGUNIT ONE SUGGESTIONS Functions REFERENCECODE I PAGE 1 IntroductionwellaTrigonometry college as in(1-1) subject. other is branches a subjectIt was ofstudiedwhich mathematics. is by important sea captains Two in hundredphysics for navigation, and yearsengineering ago, by surveyorsit was as H.... 1 practicaltoemphasis.Today,andEaster. chart the However, theassistancethe measurement analyticcolonialThis course with of treatment wilderness, observatories newaspect will navigational stress ofof trigonometryandtrigonometric thisinby calculating modern ministersmethods, has functionspoint thetodeclinedspecialization calculatedatesof view is inofreceiving as importance.Easter,the well of date surveying, asgreater theof the DirectedThe CoordinateRectangularsolution Segments of triangles. axesCoordinate (1-2) : x-axis, System y-axis (1-3) H. ... 22, 3 The DistanceQuadrantsRadiusOriginPlotting vector a Formula point (1-4) H.... 4, 5 H .SUGGESTEDpp. 5, 6 : Ex. 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HSUGGESTED"0isp. negative 7 : ASSIGNMENTEx. 1"-17 LESSON Special Right TrianglesSCOPE AND TEACHING SUGGESTIONS .CODE1REFERENCEGeometry PAGE 3 The specialb.a.30-60-905,12,133, right 4, 5 triangletriangles triangle triangle such as the AppendixRightSpecialStudyCourseTriangles of I fully.mainingthatare used theProvided.c. students sidesextensively45-45-90 of sufficient maythe trianglein bethis able practice course. when to calculate in they Thethe are30-60-90 teacher mentally given should theandthe length 45-45-90lengths review