NORTHEAST COLLEGE Department of Mathematics Plane Trigonometry COURSE SYLLABUS FOR MATH 1316 (April 2007) Professor: Israel N Nwaguru Office Phone: 713-718-2437 Office: NOLN 321 Office Hours: Northline Center: MW, 9:30-11 and TuTh 12:30 1:00; otherwise by appointment. (or hours of availability) E-mail: Israel.nwaguru@hccs.edu Website: Course Title: Plane Trigonometry Semester and Year: SPRING, 2011 Course Prefix: Math Course Number: 1316; CRN 66210 Class Days & Times: TuTh, 9:30 11:00 Credit Hours: 3 Lecture Hours: 3 Class Room Location: NOLN ROOM 226 Lab Hours: 0 External Hours: 0 Total Contact Hours: 48 (All hrs. x 16) ATTENDANCE AND DROP POLICY: Regular attendance is extremely important in mathematics classes. Attendance will be recorded for each class session. You may be dropped for excessive absences after you have accumulated absences in excess of 12.5% of the hours of instructions. For example, for a three-credit hour lecture class meeting three hours per week (48 hours of instructions), you may be dropped after six hours of absence provided that those six hours are missed prior to the official drop date. If you should decide to withdraw from the course, initiate a student drop in the office. Should your name remain on the roll at the end of the term, you must receive a grade. Home Work: Home work will be assigned regularly. Practice is absolutely essential to mastery of mathematics. Be prepared to ask questions about any problems you are unable to work and any material in the text you do not understand. Whenever possible, try to read the sections to be covered before the lecture period. All home work should be kept in loose-leaf form and available at any time for inspection. Put your name on every page of your work. Your success in this course significantly depends on practicing and understanding the home works. Although some of
Page 2 of 5 Pages the home works may not be collected but you are required to do them. Credits are earned for doing and understanding your home work. Test: There will be four ( 100 pts.) tests during the semester. The date for each test will be discussed in class. Final Examination: The final examination is comprehensive. Cheating: Cheating can result in dismissal from the entire Houston Community College System. Any student who cheats will be dropped from the course with a grade of F. Any communication, referring to books, notes, or leaving classroom during examinations will be considered cheating. Calculators: Calculators will be used on tests. You are required to bring them to class for class work and use them for home work. Late and Makeups: Absence on the day an assignment or a test is given does not excuse a student from responsibility for the assignment/test. Required assignments which are not handed in or are handed in late without valid reason will result in a penalty on the class work grade, Final Grade: You will be evaluated on your performance as follow Three tests Final Examination Total 300 pts. 100 pts. 400pts. The final grade will be determined according to the following formula: Final Grade = (3 Exams+Final Exam)/4 90-100 A 70-79 C 80-89 B 60-69 D Below 60 F Catalog Description: MATH 1316 Plane Trigonometry. Topics include solutions of triangles, Euler identity, graphing of trigonometric and inverse trigonometric functions, identities, trigonometric equations, applications including DeMoivre s Theorem, and an introduction to vector analysis. Prerequisite: MATH 1314 or the equivalent. (Plane geometry is recommended). 3 credit (3 lecture). Prerequisites: A grade of C or better in Math 1314 or the equivalent. Course Intent: This course is intended for students whose curriculum requires trigonometry as a prerequisite for higher mathematics courses. It may also be taken as a first course in trigonometry or as a review course. Students whose curricula are generally non-technical in nature may take this course as a mathematics elective if the necessary algebraic and geometric prerequisites have been met. The transferability of this course as either mathematics credit or elective credit is at the discretion of the school to which the student intends to transfer. Audience: This course is for students who need trigonometry in order to prepare for higher mathematics courses. Course Objectives: Upon completion of this course, a student should be able to: 1. Recognize the six basic trigonometric functions and understand the relationships between them. 2. Evaluate the trigonometric functions of special angles. 3. Find reference or related angles and coterminal angles. 4. Use a calculator or a table (not on exams) to find trigonometric function values of any angle. 5. Solve right triangles. 6. Convert degrees to radians and vice-versa. 7. Solve problems dealing with the application of radian measures. 8. Solve problems relating to linear and angular velocities.
Page 3 of 5 Pages 9. Recognize the graphs of the six basic trigonometric functions. 10. Know the amplitude, period, and phase shift for sine and cosine functions. 11. Sketch functions exhibiting the above properties. 12. Recognize the various identities including sum and difference angle formula, double angle formula, and half angle formulas. 13. Prove trigonometric identities using the formulas given above. 14. Solve trigonometric equations and inverse trigonometric equations. 15. Solve triangles using the sine and cosine laws. 16. Find areas of triangles. 17. Rewrite a complex number in polar form. 18. Use DeMoivre s Theorem to simplify a complex number raised to a whole number exponent. 19. Find the nth root of a complex number. 20. Solve problems dealing with vectors. 21. Recognize polar graphs. Textbook: Dugopolski, Mark, Trigonometry, Addison-Wesley, Second Edition, 2007. Course Outline: Instructors may find it preferable to cover the course topics in the order listed below. However, Instructor may choose to organize topics in any order, but all material must be covered. CHAPTER Section Numbers Approximate Time Topics Chapter 1 Angles and the Trigonometric Functions Topics to be covered include: angles, degree measure, radian measure, angle relationships, similar triangle, definitions of trigonometric functions, reference angles, problem solving, and the fundamental identity. 1.1 Angles and Degree Measure 1 hour 1.2 Radian Measure, Arc Length, and Area 1 hour 1.3 Angular and Linear Velocity 1 hour 1.4 The Trigonometric Functions 1 hour 1.5 Right Triangle Trigonometry 2 hours 1.6 The Fundamental Identity and Reference Angles 1 hour Recommend Examination 1 Chapter 2 Graphs of the Trigonometric Functions Topics to be covered include: graphs of the trigonometric functions. (6.5 hours) 2.1 The Unit Circle and Graphing 2 hours 2.2 The General Sine Wave 1 hour 2.3 Graphs of the Secant and Cosecant Functions 1 hour 2.4 Graphs of the Tangent and Cotangent Functions 1 hour 2.5 Combining Functions (Optional) Recommend Examination 2 Chapter 3 Trigonometric Identities
Page 4 of 5 Pages Topics to be covered include: coverage of fundamental trigonometric identities, verification of trigonometric identities, and identities involving multiple angles. The chapter concludes with a discussion of how to obtain the trigonometric function of products as sums. 3.1 Basic Identities 2 hours 3.2 Verifying Identities 2 hours 3.3 Sum and Difference Identities for Cosine 1 hour 3.4 Sum and Difference Identities for Sine and Tangent 1 hour 3.5 Double-Angle and Half-Angle Identities 1 hour 3.6 Product and Sum Identities (Optional) Recommend Examination 3 CHAPTER Section Numbers Approximate Time Topics Chapter 4 Solving Conditional Trigonometric Equations (7.5 hours) Topics to be covered include: complex numbers, trigonometric form of complex numbers the product and the quotient of complex numbers, powers and roots of complex numbers, and equations with complex solutions. The unit concludes with the use of DeMoivre s theorem to find roots to an equation. 4.1 The Inverse Trigonometric Functions 2 hours 4.2 Basic Sine, Cosine, and Tangent Equations 2 hours 4.3 Multiple Angle Equations 1 hour 4.4 Trigonometric Equations of Quadratic Type 1 hour Recommend Examination 4 Chapter 5 Applications of Trigonometry (8 hours) Topics to be covered include: Law of Sines, Law of Cosines, and Area. This unit concludes with vectors in a two-dimensional plane. 5.1 The Law of Sines 2 hours 5.2 The Law of Cosines 2 hours 5.3 Area of a Triangle 1 hour 5.4 Vectors 2 hours 5.5 Applications of Vectors 1 hour
Page 5 of 5 Pages Chapter 6 Complex Numbers, Polar Coordinates, and Parametric Equations Topics to be covered include: complex numbers, trigonometric form of complex numbers, the product and the quotient of complex numbers, powers and roots of complex numbers, equations with complex solutions, and working with polar coordinates. This unit concludes with graphing in the polar coordinate plane. 6.1 Complex numbers 1 hour 6.2 Trigonometric Form of Complex Numbers 1 hour 6.3 Powers and Roots of Complex Numbers 3 hours 6.4 Polar Equations 2 hours Recommend Examination 5 Comprehensive Final Examination 2 hours Departmental Policies: 1. Each instructor must cover all course topics by the end of the semester. The final exam is comprehensive and questions on it can deal with any of the course objectives. 2. Each student should receive a copy of the instructor s student syllabus for the course during the first week of class. 3. A minimum of three in class tests and a comprehensive final departmental examination must be given. The final examination must be taken by all students. 4. All major tests should be announced at least one week or the equivalent in advance. 5. The final exam must count for at least 25 to 40 percent of the final grade. 6. The final course average will be used in the usual manner (90-100 A ; 80-89 B ; 70-79 C ; 60-69 D ; Below 60 F ). 7. Either an open book or a take home major test may be given at the discretion of the instructor. 8. Any review sheet should be comprehensive and the student should not feel that classroom notes, homework and tests may be ignored in favor of the review sheet for any examination. Resource Materials: Any student enrolled in Math 1316 at HCCS has access to the Academic Support Center where they may get additional help in understanding the theory or in improving their skills. The Center is staffed with mathematics faculty and student assistants, and offers tutorial help, video tapes and computer-assisted drills. Also available is a student s Solutions manual which may be obtained from the Bookstore. Suggested Methods: It is helpful to begin each class with questions related to the material discussed and assigned homework problems. In presenting new material, it is suggested that an explanation be followed by students working examples in class. Students should be encouraged to work the review exercises at the end of each chapter. Students should be encouraged to visit the Academic Support Center at their respective colleges. Americans with Disabilities Act (ADA): Students with Disabilities: Any student with a documented disability (e.g. physical, learning, psychiatric, vision, hearing, etc.) who needs to arrange reasonable accommodations must contact the Disability Services Office at the respective college at the beginning of each semester