Math 102,104: Trigonome try and Precalculus Spring 2018 2018 Instructor Dr. Ruzanna Baytaryan Office HSLH 341 PHONE 661-362-5916 Office Hours M-TH 1:30PM 2:30PM or by appointment Email Ruzanna.baytaryan@canyons.edu Website http://www.canyons.edu/users/baytaryanr Text Precalculus by Cohen, Lee, and Sklar (7 th ed.) Mathematics is the foundation and lifebloo nearly all human endeavors. All quantitative determinations are in the hands of mathematics, and it at once follows from this that all speculation which is heedless of mathematics, which does not enter into partnership with it, which does not seek its aid in distinguishing between the manifold modifications that must of necessity arise by a change of quantitative determinations, is either an empty play of thoughts, or at most a fruitless effort. John Frederick Herbart (1776-1841), Supplies You may need a scientific/ graphing calculator for some homework exercises and for checking your work. However, no calculators will be used on quizzes tests or the final exam unless it is specified by the instructor. Math 102 Course Description Examines circular and trigonometric functions and their inverses, identities, trigonometric equations, solutions of triangles, complex numbers, vectors, and applications.. Student Learning Outcomes: By the completion of the course a student should be able to Define the six trigonometric functions and analyze them through graphing, proving identities, and solving equations.
Math 104 Course Description Course Description: Review of equations and inequalities, liner, quadratic, radical, rational, exponential, logarithmic, and trigonometric functions. Graphing various functions using transformations and properties. Solving higher degree polynomial equations. Solving systems of linear and nonlinear equations and inequalities. Applications of optimizations and operations with functions. Discussion of sequences and series, the Binomial Theorem, and mathematical induction. Designed to prepare the student for calculus series.. Student Learning Outcomes: By the completion of the course a student should be able to 1. Analyze and graph polynomial, rational, logarithmic, exponential and trigonometric functions. 2. Recognize, analyze and solve problems involving functions Homework/Quizzes Homework will be assigned at the end of each class period (See the HW assignment sheet). However, it will not be collected. Instead, there will be in-class quizzes throughout the semester. The problems on the quizzes will be taken directly from previously discusses lecture and/or homework assignments. No makeup quiz will be given under any circumstances. Your lowest quiz score will be dropped. In class Group- work Most days in class you will be assigned to work with a group 2 or 3 other students. Problems will be assigned for - your group to work on. Each group will submit one set of solutions for each assignment. No makeup group-work will be given under any circumstances. Exams You will have five chapter exams a comprehensive final exam. No makeup tests will be given under any circumstances. Do not miss them! Your lowest test score may be replaced by your final exam score to improve your final grade. I strongly recommend that you keep all homework-quizzes and exams until you receive your course grade in case you have questions regarding your grade. Grading Your final grade will be computed from your quizzes, group works, chapter tests, and your final exam scores. Any missing exam will be scored zero. The following grade-calculation grid will be used to determine your final grade. Grade Percentage Weight Total Quiz/Group Work Average X 15% (0.15) = Chapter Exam Average X 60% (0.60) = Final Exam X 25% (0.25) = Overall grade percentage in class Grading Scale: A = 90 100% B = 80 89% C = 70 79% D = 60 69% F = Below 60%
Attendance We have a lot of material to cover and understand, so regular attendance is crucial to your success in the class. Please come on time and stay for the duration of the class. If you cannot attend regularly, on time, and stay for the entire class, you should take this class at another time that fits your schedule. Students arriving late or leaving early, without authorization from the instructor, may be marked tardy. Two recorded tardies will count as one absence. Excessive absences (2 or more) may result in being dropped from the class. Expectations A collaborative and respectful environment is anticipated. I expect you to come to class with a commitment to learn and to take responsibility for your learning. This means participating in the discussions, taking notes, and helping others to learn. Please ask questions and let me know if you have difficulties. If you feel you may need an accommodation based on the impact of a disability, please contact me privately to discuss your specific needs. You will be asked to leave if you engage in any inappropriate behavior during class. Cell phones are to be turned off during class. Neither food nor drinks are allowed in the classroom with the exception of bottled water. MANAGEMENT OF STRESS AND MENTAL HEALTH: Often the pressure on our students is very strong, involving academic commitments, relationships, outside jobs and family pressure to name a few. The staff and faculty of College of the Canyons are here to see you succeed academically and care about your emotional and physical health. You can learn more about the broad range of confidential student services, including counseling and mental health services available on campus by visiting the Student Health & Wellness Center in the Student Services Building (across from the bookstore) or by clicking on http://www.canyons.edu/offices/health/pages/default.aspx. The phone number is 661-362-3259. Also, the National Suicide Hotline number is 1-800-273-8255. All students at COC are encouraged to enter that phone number in their cells. You can it call when you, or someone you know, is having thoughts of suicide or is in severe distress. Associate Degrees/Transfer Information Recent California Legislation guarantees admission to a California State University (CSU) campus for any community college student who completes an associate degree for transfer. The Associate in Science for Transfer (AS-T) in Administration of Justice, Computer Science, Geology, Mathematics, and Physics or the Associate in Arts for Transfer (AA-T) in Geography, is intended for College of the Canyons students who plan to complete a bachelor's degree in a similar major at a CSU campus. Students must earn a C or better in all courses required for the major or area of emphasis. The College also offers associate degrees in Administration of Justice, Biology, Computer Science, Engineering, Fire Technology, Math, Medical Laboratory Technician, Nursing (LVN to RN), and Registered Nursing. For more information on the suggested sequence of classes to be taken in order to obtain these degrees in two years, as well as information on when these courses are guaranteed to be offered, please visit: http://www.canyons.edu/offices/mathsciencediv/pages/classes.aspx.
Math 102 L e c t u r e O U T L I N E M-TH This schedule is tentative. It is subject to change. 1 02/05/18 Introduction 6.1 Trigonometric of Acute Angles 02/06/18 6.2 Right-Triangle Applications 6.3 Trigonometric of Angles 02/07/18 6.3 Trigonometric of Angles 02/08/18 6.4 Trigonometric Identities 2 02/12/18 7.1 Radian Measure 7.2 Trigonometric of Angles 02/13/18 7.2 Trigonometric of Angles 7.3 Evaluating the Trigonometric 02/14/18 7.4 Algebra and the Trigonometric 7.5 Right Triangle Trigonometry 02/15/18 7.5 Right Triangle Trigonometry 3 02/19/18 HOLIDAY 02/20/18 Test-1 (6.1-7.5) 02/21/18 8.1 Trigonometric of Real Numbers 02/22/18 8.3 Graphs of y Asin( Bx C) and 8.2 Graphs of Sine and Cosine y Acos ( Bx C)
4 02/26/18 8.4 Simple Harmonic Motion 8.5 Graphs of Tangent and the Reciprocal 02/27/18 8.5 Graphs of Tangent and the Reciprocal 02/28/18 9.1 The Addition Formula 9.2 The Double Angle Formula 03/01/18 Test-2 (8.1-8.5 5 03/05/18 9.2 The Double Angle Formula 9.3 The Product to Sum and Sum to Product Formulas 03/06/18 9.4 Trigonometric Equations 03/07/18 9.5 The Inverse Trigonometric 03/08/18 10.1 Right-Triangle Applications 6 03/12/18 Test-3 (9.1-9.5) 03/13/18 10.2 The Law of Sines and the Low of Cosines 03/14/18 10.3 Vectors in Plane: A Geometric Approach 03/15/18 10.4 Vectors in Plane: An Algebraic Approach 10.4 Vectors in Plane: An Algebraic Approach 7 03/19/18 10.5 Parametric Equations 03/20/18 10.6 Introduction to Polar Coordinates 03/21/18 10.7 Curves in Polar Coordinates 03/22/18 10.8 DeMoivre s Theorem 8 03/26/18 03/27/18 Final Exam Review 03/28/18 Final Exam Review 03/29/18 Final Exam Test-2 (10.1-10.8)
Math 102 Homework Assignments SECTIONS EXERCISES Chapter-6 An Introduction to Trigonometry via Right Triangles 6.1 Trigonometric of Acute Angles # 1-55 odd 6.2 Right-Triangle Applications # 1-29 odd 6.3 Trigonometric of Angles # 1-53 eoo, 55-71 odd 6.4 Trigonometric Identities # 1-49 odd Chapter-7 The trigonometric 7.1 Radian Measure # 1-33 odd, 37, 39, 41, 49 7.2 Trigonometric of Angles # 1-89 eoo 7.3 Evaluating the Trigonometric # 1-29 odd, 33 7.4 Algebra and the Trigonometric # 1-67 odd, 73-83 odd 7.5 Right Triangle Trigonometry # 1-51 odd Chapter-8 Graphs of the trigonometric functions 8.1 Trigonometric of Real Numbers # 1-55 odd 8.2 Graphs of Sine and Cosine # 1-35 odd, 57, 59 8.3 Graphs of y Asin( Bx C) & y Acos ( Bx C) # 1-29 odd, 33, 37, 41, 43, 45 8.4 Simple Harmonic Motion # 1, 3, 5
8.5 Graphs of Tangent and the Reciprocal # 1-49 odd Chapter-9 analytical trigonometry 9.1 The Addition Formula # 1-59 odd, 65-79 odd 9.2 The Double Angle Formula # 1-51 odd, 55, 57 9.3 The Product to Sum and Sum to Product Formulas # 1-41 odd, 49, 51 9.4 Trigonometric Equations # 1-73 odd, 77-83 odd 9.5 The Inverse Trigonometric # 1-45 odd, 63, 87, 89, 91 Chapter-10 additional topics in trigonometry 10.1 Right-Triangle Applications # 1, 5, 7, 9, 13, 15, 17, 25-39 odd, 45 10.2 The Law of Sines and the Low of Cosines # 1-39 odd, 43, 45, 54, 59 10.3 Vectors in Plane: A Geometric Approach # 1-45 eoo, 47, 49, 51 10.4 Vectors in Plane: An Algebraic Approach # 1-75 odd, 77 10.5 Parametric Equations # 1-25 odd 10.6 Introduction to Polar Coordinates # 1-37 odd, 47, 49 10.7 Curves in Polar Coordinates #1, 3, 5, 11-25 odd, 37 10.8 DeMoivre s Theorem # 1-61 odd, 75, 77
Math 104 L e c t u r e O U T L I N E M-TH Tis schedule is tentative. It is subject to change. 1 04/10/17 1.6 Equations of Lines 1.7 Symmetry and Graphs. Circles 2.1 Quadratic Equations: Theory and Examples (Review Complex Numbers) 04/11/17 2.2 Other Types of Equations 2.3 Inequalities 2.4 More on Inequalities 04/12/17 3.1 The Definition of a Function 3.2 The Graph of a Function 04/13/17 3.3 Shapes of Graphs. Average Rate of Change 3.4 Techniques of Graphing 2 04/17/17 3.5 Methods of Combining. Iteration 3.6 Inverse 04/18/17 Test-1 (1.6-3.4) 04/19/17 9.5 The Inverse Trigonometric 10.8 DeMoivre s Theorem 04/20/17 4.1 Linear 4.2 Quadratic 3 04/24/17 4.4 Setting Up Equations that Define 4.5 Maximum and Minimum Problems 04/25/17 4.6 Polynomial 4.7 Rational 04/26/17 5.1 Exponential 5.2 The Exponential Function y = e x 04/27/17 Test-2 (3.5, 6.6, 9.5, 10.8, 4.1-4.7) 4 05/01/17 5.3 Logarithmic 5.4 Properties of Logarithms 05/02/17 5.5 Equations and Inequalities with Logs and Exponents 5.6 Compound Interest 05/03/17 11.2 Gaussian Elimination 11.3 Matrices 05/04/17 11.4 Inverse of a Square Matrix 11.5 Determinants and Cramer s Rule
5 05/08/17 11.6 Nonlinear Systems of Equations 12.1The Basic Equations 05/09/17 Test-3 (5.1-5.7, 11.1-11.6) 05/10/17 12.2 The Parabola 12.4 The Ellipse 05/11/17 12.5 The Hyperbola 12.6 The Focus- Directrix Property of Conics 10.6 Introduction to Polar Coordinates 6 05/15/17 10.7 Curves in Polar Coordinates 12.7 The Conics in Polar Coordinates 05/16/17 13.1 Roots of Polynomial Equations 13.2 The Remainder Theorem and the Factor Theorem 05/17/17 Test-4 (12.1-12.7, 10.6, 10.7) 05/18/17 13.3 The Fundamental Theorem of Algebra 13.4 Rational Irrational Roots 7 05/22/17 13.5 Conjugate Roots and Descartes Rule of Signs 13.7 Partial Fractions 05/23/17 14.1 Mathematical Induction 14.2 The Binomial Theorem 05/24/17 14.3 Introduction to Sequences and Series 14.4 Arithmetic Sequences and Series 05/25/17 14.5 Geometric Sequences and Series 8 05/29/17 HOLIDAY 05/30/17 05/31/17 Final Exam Review 06/01/17 Final Exam Memorial Day Test-5 (13.1-13.7,14.1-14.5)
Math 104 Homework Assignment Sheet Sections and Topics Problems Chapter 1: Fundamentals 1.6 Equations of Lines 5, 7, 11-29odd, 41, 49, 53 1.7 Symmetry and Graphs. Circles 1-25odd, 47, 49, 55-61odd, 67 Chapter 2: Equations and Inequalities 2.1 Quadratic Equations. Theory and Examples 10, 14, 18, 29, 31, 35, 37, 39, 42, 43-51odd, 56, 69 2.2 Other Types of Equations 4, 6, 9, 19, 29, 31, 47, 51, 57, 70, 71, 74, 89, 91, 2.3 Inequalities 6, 7, 10, 20, 27, 38 2.4 More on Inequalities 1, 13, 21, 29, 33, 37, 49, 57, 81, 82 Chapter 3: 3.1 The Definition of a Function 9-23odd, 33, 35, 37, 45-48all, 49-59odd 3.2 The Graph of a Function 1, 5, 9, 11, 12, 19, 23-29odd, 33, 35 3.3 Shapes of Graphs. Average Rate of Change 1, 2, 4, 9-15odd, 21-31odd, 41, 43 3.4 Techniques of Graphing 1-39 odd 3.5 Methods of Combining. Iteration 1, 2, 7, 11, 13, 18, 19, 21, 23, 24, 27, 29, 31, 49 3.6 Inverse 3, 5, 7, 11, 15, 19, 21-27 odd, 37, 41, 43, 45 9.5 Inverse Trigonometric 1-19odd, 25-33odd, 35, 37, 43, 45, 59, 63, 65, 67 10.8 DeMoivre s Theorem 1-61 odd, 75, 77 Chapter 4: Polynomial and Rational. Applications to Optimization 4.4 Setting Up Equations That Define 1, 3, 7, 12, 19, 21, 33, 39, 41, 47 4.5 Maximum and Minimum Problems 1, 5, 7, 11, 13, 17, 21, 27, 29, 31, 33, 43, 45 4.6 Polynomial 3, 11-23odd, 27, 31, 33, 39, 41, 43
4.7 Rational 9, 13, 17, 21, 25, 27, 29, 39, 41, 43, 45 Chapter 5: Exponential and Logarithmic 5.1 Exponential 3-31odd, 39, 41, 45 5.2 The Exponential Function y = e x 13, 17, 23, 31, 35-41 odd, 55, 61, 63 5.3 Logarithmic 1-4all, 5-45 odd, 49, 51, 53 5.4 Properties of Logarithms 1-9 odd, 13-27odd, 51-63 odd, 71, 72, 73, 77, 81, 83 5.5 Equations and Inequalities with Logs and 1-41 eoo, 43-55 odd, 61, 63, 71, 72, 73, 77, 81, 83 Exponents 5.6 Compound Interest (Optional) 1-25odd 5.7 Exponential Growth and Decay (Optional) 7, 9, 11, 20, 25, 27, 29, 33, 35, 39, 45, 49, 55, 57, 59 Chapter 11: Systems of Equations 11.2 Gaussian Elimination 11-29odd, 39 11.3 Matrices 9, 13, 17, 21, 23-51 eoo, 57 11.4 The Inverse of a Square Matrix 1, 5, 17, 19, 25, 33, 35 11.5 Determinants and Cramer s Rule 3, 5, 15, 17, 19, 33, 35, 37, 39, 43, 51, 55, 58 11.6 Nonlinear Systems of Equations 3, 7, 11, 13, 17, 19, 22, 37, 39, 40 Chapter 12: The Conic Sections 12.1 The Basic Equations 8, 9, 11, 13, 17, 21, 25, 27, 28, 29, 39, 45 12.2 The Parabola 11, 13, 17, 19, 25, 29, 31, 33, 35, 37, 39, 43 12.4 The Ellipse 1, 7, 17, 19, 23-35odd, 43, 46, 49, 51 12.5 The Hyperbola 9, 15, 21, 23-39odd, 44, 49 12.6 The Focus-Directrix Property of Conics 1-15odd 10.6 Introduction to Polar Coordinates 1, 3, 5, 6, 7-23odd 10.7 Curves in Polar Coordinates 13-27odd, 36, 37 12.7 Conics in Polar Coordinates Chapter 13: Roots of Polynomial Equations 13.1 Divisions of Polynomials 1-37 eoo, 39, 53, 55 13.2 The Remainder and the Factor Theorems 5, 11, 13, 21, 23, 31, 37, 47-53odd, 55, 57
13.3 The Fundamental Theorem of Algebra 1, 13, 15, 17, 19, 24, 31, 33, 35, 39, 42, 45 13.4 Rational and Irrational Roots 3, 5, 9, 13, 17, 19, 23, 25, 29, 31, 33 13.5 Conjugate Roots and Descartes Rule of Sings 5, 11, 13, 17, 19, 25, 34, 37, 41, 43, 44 13.7 More About Partial Fractions 7, 11, 15, 17, 25, 29, 33, 39, 47, 53 Chapter 14: Additional Topics in Algebra 14.1 Mathematical Induction 3, 5, 9, 13, 15, 17, 19, 21, 35, 37 14.2 The Binomial Theorem 4, 10, 13, 17, 23, 25, 28, 29, 39-49 odd 14.3 Introduction to Sequences and Series 11, 13, 17, 18, 21, 23, 29, 37, 39, 43, 45, 49-61odd, 14.4 Arithmetic Sequences and Series 2, 3, 7, 9, 11, 13, 16, 19, 21-29 odd,35 14.5 Geometric Sequences and Series 1, 3, 9, 11, 13, 14, 17, 19, 21, 27, 29, 31, 35