EASTERN ARIZONA COLLEGE Precalculus Trigonometry

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1 EASTERN ARIZONA COLLEGE Precalculus Trignmetry Curse Design Curse Infrmatin Divisin Mathematics Curse Number MAT 181 Title Precalculus Trignmetry Credits 3 Develped by Gary Rth Lecture/Lab Rati 3 Lecture/0 Lab Transfer Status ASU NAU UA MAT Dept Elective, Mathematics (MA) MAT Departmental Elective als satisfies: Science/Applied Science [SAS] MATH 111 Activity Curse N CIP Cde Assessment Mde Pre/Pst Test (25 Questins/100 Pints) Semester Taught Fall and Spring GE Categry Mathematics Separate Lab N Awareness Curse N Intensive Writing Curse N Prerequisites MAT 154 with a grade f "C" r higher r cncurrent enrllment in MAT 154 r placement test scre as established by District plicy and ENG 091 with a grade f C r higher r reading placement test scre as established by District plicy Educatinal Value Apprpriate fr students whse majr is Mathematics, Physics, Chemistry, r Engineering. Descriptin Trignmetric functins, identities and equatins; develpment and applicatin f the varius frmulae fr slving triangles, vectrs, and cmplex numbers. Supplies Scientific Calculatr EASTERN ARIZONA COLLEGE Precalculus Trignmetry Equal Opprtunity Emplyer and Educatr

2 Cmpetencies and Perfrmance Standards 1. Apply techniques f angle measures t develp and use trignmetric functins and Pythagrean identities. Learning bjectives What yu will learn as yu master the cmpetency: a. Understand degree measure f angles and calculate cterminal angles. b. Apply prperties f similar triangles t the slving f applicatin prblems. c. Define the trignmetric functins fr quadrantal angles and nn-quadrantal angles. d. Use the definitins f trignmetric functin t develp and use reciprcal, qutient, and Pythagrean identities. Perfrmance Standards Yu will demnstrate yur cmpetence: n assigned activities n written exams n a tw-hur cumulative final exam Yur perfrmance will be successful when: learner finds the measure f an angle in degrees learner finds the measure f c-terminal angles in degrees learner slves applied prblems using similar triangles learner states the values f the six trignmetric functins fr a given angle learner states the reciprcal, qutient, and Pythagrean identities and uses them t find trignmetric functin values 2. Apply techniques invlving right triangle ratis t slve fr unknwn quantities such as angle measures and side lengths. Learning bjectives What yu will learn as yu master the cmpetency: a. Slve angle f elevatin and angle f depressin prblems. b. Slve bearing prblems. c. Relate trignmetric functins t angle and real number dmains. d. Apply special reference triangle and angle prperty rules f degree and 45 degree right triangles t slve applicatin prblems. Perfrmance Standards Yu will demnstrate yur cmpetence: n assigned activities n written exams n a tw-hur cumulative final exam Yur perfrmance will be successful when: learner defines the basic trignmetric functins n the set f real numbers learner uses a reference triangle t find the unknwn infrmatin f a given trignmetric applicatin prblem learner slves angle f elevatin, angle f depressin, and bearing prblems learner slves fr unknwn quantities f similar r right triangles by applying the apprpriate EASTERN ARIZONA COLLEGE Precalculus Trignmetry Equal Opprtunity Emplyer and Educatr

3 algebraic and trignmetric slving techniques 3. Apply techniques f trignmetric functins t slve prblems fr linear and angular velcity in bth degree and radian measure. Learning bjectives What yu will learn as yu master the cmpetency: a. Apply algebraic techniques t calculate lengths f arcs and t cnvert between radian and degree measure f angles. b. Apply algebraic techniques t cnvert between linear and angular measures f velcity. c. Define circular functins with their assciated dmain, range, and peridic prperties. d. Apply principles f linear and angular mtin t the slutin f prblems invlving linked wheels and gears. Perfrmance Standards Yu will demnstrate yur cmpetence: n assigned activities n written exams n a tw-hur cumulative final exam Yur perfrmance will be successful when: learner finds the measure f an intercepted arc given either a central r an inscribed angle measure learner finds the measure f an angle given the measure f an intercepted arc and that the angle is either a central r an inscribed angle learner sketches the basic trignmetric functins n a unit circle learner cnverts crrectly between linear and angular velcity values learner states the dmain, the range, and the perid fr any trignmetric r circular functin learner cmputes the value f a circular functin 4. Apply basic graphing techniques t sketch graphs f trignmetric functins. Learning bjectives What yu will learn as yu master the cmpetency: a. Graph all the basic trignmetric functins and state the apprpriate dmain, range, amplitude and perid fr each graph f: Sine, Csine, Tangent, Csecant, Secant and Ctangent. b. Graph trignmetric functins cntaining altered phase shift and amplitude values. Perfrmance Standards Yu will demnstrate yur cmpetence: n assigned activities n written exams n a tw-hur cumulative final exam Yur perfrmance will be successful when: learner sketches all basic trignmetric functins and state the apprpriate infrmatin fr dmain, range, amplitude, and perid learner sketches a trignmetric functin in the frm f y = k + Asin(Bx + C) r y = k + EASTERN ARIZONA COLLEGE Precalculus Trignmetry Equal Opprtunity Emplyer and Educatr

4 Acs(Bx + C) learner sketches the c-functin f any basic trignmetric functin and state the apprpriate infrmatin fr dmain, range, amplitude and phase shift 5. Apply basic fundamental trignmetric identities t verify and prve the ther trignmetric identities; sum, difference, c-functin, duble-angle, half-angle, prduct-sum and sumprduct. Learning bjectives What yu will learn as yu master the cmpetency: a. Apply basic trignmetric identities and prperties f algebra t prve whether a given statement is valid. b. Apply basic trignmetric identities and algebraic prperties t prve the validity f cmplex and cmpund trignmetric identities. c. Exhibit an understanding f the nature, cnstructin and reasning f an elementary trignmetric prf. Perfrmance Standards Yu will demnstrate yur cmpetence: n assigned activities n written exams n a tw-hur cumulative final exam Yur perfrmance will be successful when: learner cnstructs a tw clumn prf cntaining steps and assciated reasns learner writes a prf which verifies the validity f a stated identity learner cnstructs prfs f nntrivial trignmetric identities 6. Apply slving techniques fr inverse trignmetric functins, equatins, and inequalities. Learning bjectives What yu will learn as yu master the cmpetency: a. Explain hw inverse trignmetric functins facilitate the slving f trignmetric functins. b. Apply inverse trignmetric and algebraic slving techniques n trignmetric functins t find specified infrmatin. c. Cnstruct a graph shwing the basic trignmetric functin and the apprpriate inverse functin with accmpanying dmain, range, and amplitude and perid infrmatin. d. Cnstruct a graph shwing a trignmetric functin and the inverse trignmetric functin where amplitude, perid, and phase shift have been altered frm the basic frm. Perfrmance Standards Yu will demnstrate yur cmpetence: n assigned activities n written exams n a tw-hur cumulative final exam Yur perfrmance will be successful when: learner cnstructs a graph fr each basic inverse trignmetric functin and state the apprpriate dmain, range, amplitude, perid and phase shift learner cnstructs an inverse trignmetric functin graph fr a given nntrivial trignmetric EASTERN ARIZONA COLLEGE Precalculus Trignmetry Equal Opprtunity Emplyer and Educatr

5 functin graph learner slves trignmetric equatins by applying inverse slving techniques 7. Apply slving techniques using the law f Sines, Csines and vectrs t find missing infrmatin in applicatin prblems. Learning bjectives What yu will learn as yu master the cmpetency: a. Apply the laws f Sines and Csines t find missing angles and sides fr any given triangle. b. Apply frmulas fr finding areas f triangles with varius types f given infrmatin. c. Define vectrs as directed line segments in the plane and as tw cmpnent gemetric bjects. d. Apply algebraic techniques t cmbine tw cmpnent bjects. e. Exhibit an understanding f the interplay between vectrs as gemetric bjects and vectrs as directed line segments. f. Apply slving techniques f directed gemetric vectrs t find slutins fr angle measurement, directin and distance measurement in applicatin prblems. Perfrmance Standards Yu will demnstrate yur cmpetence: n assigned activities n written exams n a tw-hur cumulative final exam Yur perfrmance will be successful when: learner finds missing angles and sides f a triangle by using the laws f Sines and Csines learner finds the areas f given triangles by using given base and height infrmatin, length f tw sides and included angle; r Hern's frmula fr three given sides learner crrectly cmbines tw cmpnent parts using additin, subtractin, multiplicatin, divisin, scalar, and dt prduct prcedures learner crrectly cmputes frm tw given vectrs the length f the resultant vectr and the measure f the included angle learner crrectly cnstructs and slves a directed gemetric mdel f an applicatin prblem Types f Instructin Classrm Presentatin Grading Infrmatin Grading Ratinale Each instructr has the flexibility t develp evaluative prcedures within the fllwing parameters. 1. Written exams must represent at least 60% f the final curse grade 2. Final exam must represent at least 20% f the final curse grade. 3. The Pst Test is t be embedded in the final exam and must represent at least 10% f the final curse grade. 4. Other activities may represent at mst 20% f the final curse grade. EASTERN ARIZONA COLLEGE Precalculus Trignmetry Equal Opprtunity Emplyer and Educatr

6 Grading Scale A 90%-100% B 80%-89% C 70%-79% D 60%-69% F Belw 60% EASTERN ARIZONA COLLEGE Precalculus Trignmetry Equal Opprtunity Emplyer and Educatr