Trigonometry and Analytic Geometry

Transcription

1 Trigonometry and Analytic Geometry MATH 133 A (Hybrid Course) Syllabus - Fall 2013 Instructor: Office : Office hours: Class hours: Course website: Dr. Seongchun Kwon( Michelle) skwon@unionky.edu To be decided To be decided 2:30 PM-3:50 PM Thursday, 102 Miller Hall ULearn Text and On-Line HW Calculator: Course Description: Effective Study procedure: Cengage Learning and WebAssign (ISBN # ) The included features are e-book(trigonometry 9th Ed. ( ISBN ) Authors: Ron Larson, Publisher: Brooks/Cole) and on-line HW. You are to purchase at the College bookstore. *You can print out up to 10 pages from e-book each day. Any scientific calculator * Cell phones are not to be used for calculation purpose during Exam. This course emphasizes the problem solving on various topics in Trigonometry and Analytic Geometry. Many materials covered in this course help prepare you for the Calculus sequence. Topics to be covered are right triangle ratios, trigonometric functions, graphing trigonometric functions, identities, inverse trigonometric functions, laws of Sines and Cosines, polar coordinates and complex numbers, analytic geometry. 1. Learn what sections you are to study by referring to the schedule. 2. Watch the video clips in the sections you have to learn in the corresponding week. Take a note. 3. Read the related Powerpoint lecture note. Clarify further details of the Powerpoint lecture note and make your own note. Refer to the e- book, video lectues and video lecture note you have taken while you do this. 4. Repeat 2 and 3 in the procedure until you understand the materials. 5. Finish WebAssign HW. *You can attempt to solve the HW problem set up to 5 times. The best score will be recorded.

2 Homework: Exam Class Attendance: Assessment: There will be weekly on-line homework. Please login to WebAssign and follow the weekly homework schedule. *If you experience any technical problem with WebAssign, then you are to contact at (800) Further information is available in the WebAssign Student Support website which is linked in our course website. There will be three in-class exams. The 3 rd exam will be comprehensive final exam whose range covers all semester s matrials. You are to come to class on the first day of the class and exam days. Otherwise, attendance of the class is not mandatory unless I inform you to do so. However I will be in the classroom throughout the class hour to get your questions and to discuss the problem solving if you come to get help. I strongly encourage you to utilize class hours effectively by coming. Please study the assigned weekly materials before you come to class. The course grade is based on Homework(100 pt), 2 Midterm exams(100 pt each), Final exam( 200 pt ). Grade A : B : C : D : F : Help: On-line Tutoring Academic Honesty: Accomodation for Students with Disability Please, do not hesitate to come to my office during office hours and ask me questions. However, I want to see what attempts you have made to solve problems or what are the particular points you have diffculties in understanding. I will be very pleased to see your efforts in this course. However, I am not willing to go through HW problems like your private tutor. Study hard. But do not depend on others. SMARTthinking is an on-line tutoring service. You can ask questions to tutors any time you want. Otherwise announced, the service is available 24/7. You can reach the tutoring service site through ULearn. Union College expects a high standard of academic integrity. Academic dishonesty, such as plagiarism, unauthorized collaboration, or cheating, undermines the academic integrity of each student and of the institution by violating the spirit of a true learning community and, therefore, will not be tolerated. Students with disabilities who require accommodations (academic adjustments and/or auxiliary aids or services) for this course should contact the Director of Student Support Services, Centennial Hall, Room 104. The phone number is Students with disabilities should request accommodations prior to or early in the semester. Each request for

3 accommodations will be examined on a case-by-case basis to determine eligibility. DO NOT request accommodations directly from the professor or instructor. Professors and/or instructors are NOT authorized to make reasonable accommodations. Statement The only authorized address for academic, administrative, and cocurricular communications between Union College and its students is through the <unionky.edu> system. Each student is responsible, for monitoring his/her Union College account frequently (preferably daily). Please contact me by an rather than by phone. Under normal circumstances, a student can expect a response to an within 48 hours. However, it is very likely to return your in 24 hours. Course Availability: Minimum Technology Requirements: Emergencies or Interruption in Internet Service Students will be able to access this course from the course start date through the end of the term through Moodle. In compliance with the TEACH Act, students who complete the course will not be able to access the course site in Moodle once the course ends. Students are therefore encouraged to maintain personal records of any assignments, grade history, etc. that they wish to retain for future purposes. This course is an on-line course. Internet access is essential to watch YouTube video lecture clips, print out powerpoint and complete on-line HW. Powerpoints are posted as pdf files. You are to install Adobe Acrobat which is free software. Unexpected problems and emergencies may occur in online learning as they do in any learning environment. Have a backup plan for completing course work, such as using the computers at a local library, in case your computer crashes or your Internet service is interrupted. In addition, it is wise to save backup copies of any material that you post online. When emergencies interfere with deadlines, please contact me so that we can arrange an extension or alternate way of completing an assignment.

4 Trigonometry and Analytic Geometry MATH 133 A (Hybrid Course) Tentative Schedule-Fall 2013 Week Date Materials Covered 1 Aug 27 - Sep 1 Introduction( Course information, Introduction to WebAssign) 1.1. Radian and Degree Measure 2 Sep 2 - Sep Trigonometric Functions: The Unit Circle 1.3. Right Triangle Trigonometry 3 Sep 9 - Sep Trigonometric Functions of Any Angle 1.5. Graphs of Sine and Cosine Functions 4 Sep 16 - Sep Graphs of Other Trigonometric Functions 1.7. Inverse Trigonometric Functions 5 Sep 23 - Sep Inverse Trigonometric Functions 2.1. Using Fundamental Identities 6 Sep 30 - Oct 6 Review for the Exam Exam 1( ) 7 Oct 7 - Oct Verifying Trigonometric Identities 2.3. Solving Trigonometric Equations 8 Oct 14 - Oct Solving Trigonometric Equations 2.4. Sum and Difference Formulas 9 Oct 21 - Oct Multiple-Angle and Product-to-Sum Formulas 3.1. Law of Sines 10 Oct 28 - Nov Law of Cosines 3.3. Vectors in the Plane 11 Nov 4 - Nov Vectors and Dot Products Review for the Exam 2 12 Nov 11 - Nov 17 Exam 2( ) 4.1. Complex Numbers 13 Nov 18 - Nov Complex Solutions of Equations 4.3. Trigonometric Form of a Complex Number 14 Nov 25 - Dec DeMoivre's Theorem, 6.6. Parametric Equations

5 (Thanks Giving) 15 Dec 2 - Dec Polar Coordinates, Exam 3(Comprehensive exam: all semester s materials) 16 Dec 9 - Dec 13

6 Trigonometry and Analytic Geometry MATH 133 A (Hybrid Course) Learning Objective-Fall 2013 Sections Course Outcome (After the completion of the section, students will be able to ) 1.1. Radian and Degree Measure Describe angles. Use radian measure. Use degree measure. Use angles to model and solve reallife problems Trigonometric Functions: The Unit Circle Identify a unit circle and describe its relationship to real numbers. Evaluate trigonometric functions using the unit circle. Use the domain and period to evaluate sine and cosine functions. Use a calculator to evaluate trigonometric functions Right Triangle Trigonometry Evaluate trigonometric functions of acute angles. Use fundamental trigonometric identities. Use a calculator to evaluate trigonometric functions. Use trigonometric functions to model and solve real-life problems Trigonometric Functions of Any Angle Evaluate trigonometric functions of any angle. Find reference angles. Evaluate trigonometric functions of real numbers Graphs of Sine and Cosine Functions Sketch the graphs of basic sine and cosine functions. Use amplitude and period to help sketch the graphs of sine and cosine

7 functions. Sketch translations of the graphs of sine and cosine functions. Use sine and cosine functions to model real-life data Graphs of Other Trigonometric Functions Sketch the graphs of tangent functions. Sketch the graphs of cotangent functions. Sketch the graphs of secant and cosecant functions. Sketch the graphs of damped trigonometric functions Inverse Trigonometric Functions Evaluate and graph the inverse sine function. Evaluate and graph the other inverse trigonometric functions. Evaluate and graph the compositions of trigonometric functions Using Fundamental Identities Recognize and write the fundamental trigonometric identities. Use the fundamental trigonometric identities to evaluate trigonometric functions, simplify trigonometric expressions, and rewrite trigonometric expressions Verifying Trigonometric Identities Verify trigonometric identities Solving Trigonometric Equations Use standard algebraic techniques to solve trigonometric equations. Solve trigonometric equations of quadratic type. Solve trigonometric equations involving multiple angles. Use inverse trigonometric functions to solve trigonometric equations Sum and Difference Formulas Use sum and difference formulas to evaluate trigonometric functions, verify identities, and solve

8 trigonometric equations Multiple-Angle and Product-to-Sum Formulas Use multiple-angle formulas to rewrite and evaluate trigonometric functions. Use power-reducing formulas to rewrite and evaluate trigonometric functions. Use half-angle formulas to rewrite and evaluate trigonometric functions 3.1. Law of Sines Use the Law of Sines to solve oblique triangles (AAS or ASA). Use the Law of Sines to solve oblique triangles (SSA). Find the areas of oblique triangles. Use the Law of Sines to model and solve real-life problems Law of Cosines Use the Law of Cosines to solve oblique triangles (SSS or SAS). Use the Law of Cosines to model and solve real-life problems. Use Heron s Area Formula to find the area of a triangle Vectors in the Plane Represent vectors as directed line segments. Write the component forms of vectors. Perform basic vector operations and represent them graphically. Write vectors as linear combinations of unit vectors. Find the direction angles of vectors. Use vectors to model and solve reallife Vectors and Dot Products Find the dot product of two vectors and use the properties of the dot product. Find the angle between two vectors

9 and determine whether two vectors are orthogonal. Write a vector as the sum of two vector components. Use vectors to find the work done by a force Complex Numbers Use the imaginary unit i to write complex numbers. Add, subtract, and multiply complex numbers. Use complex conjugates to write the quotient of two complex numbers in standard form. Find complex solutions of quadratic equations Complex Solutions of Equations Determine the numbers of solutions of polynomial equations. Find solutions of polynomial equations. Find zeros of polynomial functions and find polynomial functions given the zeros of the functions Trigonometric Form of a Complex Number Plot complex numbers in the complex plane and find absolute values of complex numbers. Write the trigonometric forms of complex numbers. Multiply and divide complex numbers written in trigonometric form DeMoivre's Theorem Use DeMoivre s Theorem to find powers of complex numbers. Find n th roots of complex numbers Parametric Equations Evaluate sets of parametric equations for given values of the parameter. Sketch curves that are represented by sets of parametric equations. Rewrite sets of parametric equations as single rectangular equations by

10 eliminating the parameter. Find sets of parametric equations for graphs Polar Coordinates Plot points on the polar coordinate system. Convert points from rectangular to polar form and vice versa. Convert equations from rectangular to polar form and vice versa.