Proposed Course Outline - Trigonometry

PROPOSED COURSE OUTLINE Instructor: Arlan Rodrigo e-mail: [email protected] Course Number: Course Title: Course Credit: Course Requirements: Passing Grade: Consultation Hours: Main Reference:

Math 14 COLLEGE TRIGONOMETRY 3 3 Long Exams = 2/3 of Final Grade 1 Final Exam = 1/3 of Final Grade Attendance, Participation, Quizzes, Homework (Bonus points for Exams) 60% By appointment (send me an e-mail) Modern Algebra and Trigonometry Third Edition (Vance)

Course Objectives: At the end of the course, the student is expected to know the basic concepts of College Trigonometry. In particular, the student is expected to know the following: • • • • • • • • •

Basic concepts in Set Theory The Geometry of Real Numbers, The Cartesian Plane, The Circle Relations and Functions and differentiate them from each other The Circular Functions Inverse Circular Functions Graphs and Applications of Circular Functions The Law of Sines and the Law of Cosines and problem-solving involving Oblique Triangles Complex Numbers and Vectors Powers and roots of Complex Numbers

Exams: There will be 3 written Long Exams with a cumulative weight of 2/3 of the Final Grade. Aside from this, a Final Exam will be given at the end of the semester and this will make up 1/3 of the Final Grade. The passing grade at the end of the semester is 60%. Standard college rules will be used in determining the Final Grade to be marked in the grading sheet. Exemption from the Final Exam: If the student has obtained an average of 80% or higher for the 3 Long Exams, he/she can opt not to take the Final Exam. If he/she does so, then the Final Grade will be the average for the 3 Long Exams. Attendance, Participation, Quizzes, Homework: Extra Bonus points or percentage points will be given to students who have a good attendance. Points Earned from quizzes and homework also have their corresponding merit in the Examinations. Please refer to the table at the end for more information.

Class Policy: 1. If a student is late for more than 15 minutes for a particular class period, then he will be marked absent for that period. 2. There will be no make-up for missed quizzes and unsubmitted homework or homework submitted past the deadline. 3. If a student misses a Long Exam for a valid reason (requires documentation), then he/she must take the Final Exam and the grade for the missed Long Exam will be the grade of the Final Exam. If a student misses a second Long Exam, then it is automatically ZERO regardless of the reason. A student who misses an exam for an invalid reason will have a grade of ZERO for that exam. 4. Cheating, in any form, including copying homework will not be tolerated. COURSE OUTLINE Meeting No.

Topic

Reference/s

1

Self-Introduction by the teacher and the students, discussion of class policies, Overview of the subject / History of trigonometry Sets and basic notation, subsets and counting, operations on sets The Geometry of Real Numbers, the Cartesian Plane, the Distance Formula and the Slope Formula The Circle, ( review plus QUIZ ) Functions and Relations, Graphical Representation of Functions and Relations Definitions of the Circular Functions, Behavior of the Sine and Cosine Functions Values of the Circular Functions of Special Real Numbers, Exact Values of the Circular Functions for θ=π/5 The fundamental circular function identities, Proof of the formula for cos ( A – B ) Special Reduction Formulas, General Addition Formulas, General Reduction Formulas General Identities, Conversions of Sums and Products Function values of any number, Approximations of Function Values for small numbers

Wikipedia / other external sources

Reading assignment

Vance ( pages 2 – 15 )

YES

Vance ( pages 71 – 86 )

YES

2 3 4 5 6 7 8 9 10 11 12

EXAM 1

13 14 15

Inverse Functions, Graphing of certain relations Inverse Circular Functions Operations involving inverse circular functions, graph of the curve y = a sin kx Graph of the curves y = a sin (kx + b), graphing by addition of ordinates Simple Harmonic Motion Addition of Two General sine functions, short discussion of Harmonic Analysis and Synthesis The Algebra of Complex Numbers, The geometry of Complex Numbers The Algebra of Ordered Pairs, The Algebra of Vectors

16 17 18 19 20

Vance ( pages 86 – 93 ) Vance ( pages 95 – 106 )

Quiz

YES YES

Vance ( pages 108 – 120 ) Vance ( pages 120 – 125 )

YES YES

Vance ( pages 126 – 130 ) Vance ( pages 131 – 138 )

YES YES

Vance ( pages 139 – 145 )

YES YES

Vance ( pages 145 – 152 )

YES

Vance ( pages 266 – 272 ) Vance ( pages 272 – 276 ) Vance ( pages 276 – 278 ) Vance ( pages 332 – 333 ) Vance ( pages 334 – 336 )

YES YES YES

Vance ( pages 336 – 338 ) Vance ( pages 339 – 343 )

YES

YES YES

Vance ( pages 156 – 162 ) Vance ( pages 162 – 170 )

Homework

YES YES

21

EXAM 2

27 28 29

EXAM 3

30 31 32

Review For Final Exam ( Sample Exam to be given ) Review for Final Exam

26

Homework

Vance ( pages 346 – 354 ) Vance ( pages 355 – 363 ) Vance ( pages 363 – 366 ) Vance ( pages 366 – 374 )

YES YES

YES

Vance ( pages 374 – 382 )

YES

Reference/s

Angles, Circular functions of angles Geometric use of Angles Powers and roots of complex numbers General discussion of triangle solutions, The Law of Sines The Law of Cosines, Applications involving Oblique Triangles More problems on Oblique Triangles Additional Topic: “Trigonometric Delights”

22 23 24 25

Quiz

Topic

Meeting No.

YES YES

YES Trigonometric Delights by Eli Maor

FINAL EXAM

33 34 35 BONUS POINTS !!! CRITERIA Attendance

Per 5 classes attended : + 1% in Long Exam Complete Attendance : + 1% in Final Exam

Quizzes

Per 10 points earned : + 1% in Long Exam 90% and up for total : + 3% in Final Exam

Homework

Per 15 points earned : + 1% in Long Exam 95% and up for total : + 1% in Final Exam

YES