Science, Technology, Engineering and Math

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1 School: Course Number: Course Name: Credit Hours: Length of Course: Prerequisite: Science, Technology, Engineering and Math MATH-111 College Trigonometry 3 Credit Hours 16 weeks While there are no pre-requisites for MATH111, the course assumes the student has completed MATH110 College Algebra or an equivalent course. Course Description Course Scope Course Objectives Course Delivery Method Course Resources Evaluation Procedures Grading Scale Course Outline Policies Academic Services Course Description (Catalog) This is a course in college trigonometry. It builds on earlier college algebra courses such as MATH110, extends the students' studies to trigonometry, and introduces topics in analytical geometry. Practical applications are provided throughout the course. The course begins by reviewing methods of graphing and solving linear and quadratic functions as well as techniques for solving polynomials. It then concentrates on various trigonometric functions, identities and equations as well as the application of trigonometry to real-life situations. The final part of the course includes exponential and logarithmic functions as well as selected topics in analytic geometry including polar coordinates and the conic While there are no pre-requisites for MATH111, the course assumes the student has completed MATH110 College Algebra or an equivalent course. Course Scope This course is presented online through the APUS It uses a specially developed online text and workbook and is supplemented by video lectures covering each of the key

2 mathematical skills needed to succeed in the course. The course is organized into distinct parts. The first part of the course reviews the basics of algebra and graphing. The second part of the course investigates trig functions to include angular measure, right triangles, sine and cosine functions and graphing trig functions. The third part of the course concentrates on trigonometric identities and the applications of trigonometry. The fourth part will consider the topics of complex numbers, complex numbers in trig form, and polar coordinates. The fifth part of the course will include the application of exponential and logarithmic functions. The study of conic sections will be the sixth and final part of the course. Course Objectives After completing the course, the student should be able to accomplish the following Course Objectives (CO): CO-1 Apply the basic concepts of trigonometry to circular functions CO-2 Analyze problems using trigonometric identities, inverse functions, and equations. CO-3 Solve problems using triangles, and vectors. CO-4 Evaluate problems using logarithms and exponential functions. CO-5 Apply concepts of conic sections to practical applications. Course Delivery Method This mathematics course delivered via distance learning will enable students to complete academic work in a flexible manner, completely online. Course materials and access to an online learning management system will be made available to each student. Assigned faculty will support the students throughout this sixteen-week course. This course will be presented using a series of video lectures supplemented with a specially designed workbook available online. The weekly lectures will be on short selected topics. The total lecture time will be 1-2 hours per week. Online practice exercises, notes and animations will be available to supplement the lectures and online workbook. The nature of an online course requires a significant amount of independent work. The student will be provided with structure, resources, guidance and instructor experience for learning the course material. The student, however, is responsible for managing time, completing assignments on time, completing the readings, and making inquiries as needed to complete the course effectively. This is a 16-week course, which means the material must be learned in a relatively short period. This requires dedication and diligence on the part of the student.

3 It is important for the student to check and read the weekly Announcements for each week s work. Additional readings, internet-work and assignments will be posted online in weekly lessons in the online classroom. Assignment due dates will be posted with assignment directions. All assignments will have due dates of a week or more, therefore, no extensions or last-minute exceptions are anticipated. The student is expected to complete all work on time. Online assignments are due by 11:55 PM Eastern time on the due date for the assignment. This includes Discussion forum questions and activities, examinations, and individual assignments submitted for review or grading by the instructor. The University requires that each student contact their instructor at least weekly during the semester, which in this course will be necessary to complete all assignments. Due to the busy student schedules, all work and discussions are asynchronous, meaning students are not required to be online at a specific time with the instructor or other students. Instead, students may post comments or questions on the discussion forums as they are available each week. Students may, of course, interact with the professor or other students via the chat room at any time or with the professor during office hours or by appointment. Each student is responsible for the following: Completely reading the syllabus. Should questions arise about the syllabus or the course that are not covered or should the student need clarification, the instructor may be contacted via or in the Discussion forums. Reading for important updates and course information each week. Reading the assignments in a timely manner to ensure all questions concerning all assignments and the Final Exam are specifically addressed. Watching the assigned video lectures and working the practice problems. Checking the Announcements in the online classroom at the beginning of each week. Completing assignments on time. Students will deliver completed assignments in the mode specified by the instructor. The details for each of these can be found in this syllabus and the Weekly Announcements. Submitting all assignments, completing the discussion forum activities and submitting the final exam on time. These are the graded submissions. Students should complete these during the time periods assigned for each of them. These should be submitted by 11:55 PM Eastern Time on the due date announced by the professor. Course Resources

4 Required Course Textbooks - Thinkwell Trigonometry Companion Workbook which is available inside the classroom and within the Thinkwell course. This workbook can be downloaded onto the student s computer from within the classroom. Web Sites In order to use the video presentations, each student s computer should have a color monitor with 16 bit color or greater video card; 800x600 pixels or greater monitor resolution; soundcard; speakers or headphones. PCs should be Pentium 200 MHz or faster with Windows 96, 98, 2000, NT 4.0, XP or later; 128 MB RAM. MAC should have Power PC 120 MHz or faster with Mac OS 8.1 or later and 128 MB RAM. Thinkwell will send an with the necessary access codes prior to the start of class. Students who have not received information from Thinkwell by the first day of class should contact Students should check their SPAM filters in case it was mistakenly filed there by their provider. Both video presentations and practice problems for each section of the book are available through the Thinkwell There are also additional practice problems in the workbook. Working these problems is a good way to get feedback on how well you understand the material. The site also provides hints on how to get the answers to problems you miss. These practice problems are not part of the evaluation process but are an important factor in success at mastering the subject. Math is not a spectator sport - one learns math by putting the pencil to the paper! Students will need a scientific calculator which includes the trig functions to successfully complete this course. The calculator should include a memory and square root function. At the student s discretion, a computer spreadsheet program like Microsoft Excel may be used. Students may make use of the above for all graded assignments during the course. Evaluation Procedures Student grades for the course will be based on class participation in 16 Forums, 14 online unit tests and a timed online Final Exam.

5 Class Participation: The University requires weekly contact from each student. This requirement can be met by taking the Unit Tests and by participation in the Forums. A total of 10% of the final grade will be based on participation in the Forums. Unit Tests: There will be 14 short graded tests during the course, each of which will count as 5% of the final grade. They will be open book and open note tests, however, you may not receive any help from another person. These tests will consist of problems similar to those in the online practice problems at thinkwell.com. They are selected to provide the student with hands on experience in applying the techniques and models being discussed. Final Examination: The final exam will count as 20% of the final grade. It will be an online, openbook, open-note exam. You may not consult with any other person while taking the exam. This examination will be based on all material covered during the course of the semester. Please coordinate with the professor for any special arrangements. Unless the professor approves alternate arrangements, students should plan to take the final examination during the last week of the course. You will not need a proctor to take this exam. Assignment Deadlines: Students must plan and manage competing demands and priorities on their time and are expected to submit classroom assignments on time. Assignment due dates and times are explained in the Lessons. All assignments must be submitted by the last day of class unless you have an approved course extension. Instructors will submit student course grades to the University within seven days after the end of the semester. Official grades will continue to be issued by the University on the grade report form. Task % of Final Grade Forums 10% Unit 01 Test 5% Unit 02 Test 5% Unit 03 Test 5% Unit 04 Test 5% Unit 05 Test 5% Unit 06 Test 5% Unit 07 Test 5% Unit 08 Test 5% Unit 09 Test 5% Unit 10 Test 5% Unit 11 Test 5% Unit 12 Test 5% Unit 13 Test 5% Unit 14 Test 5%

6 Final Examination 20% Total 100% 16 Week Course Outline Please see the Student Handbook to reference the University s grading scale. Week Topic Course Objectives Readings Assignment Algebraic Prerequisites 1 Use the Cartesian system Find the distance between two points Workbook: pp Sections 1.1 to 1.7 First required contact Introduce yourself to your classmates in the discussion forum 1 Explain the collinearity and distance Write the center-radius form of a circle Solve problems involving circles Graph equations by locating points Find the x and y intercepts of a line Explain and use the vertical line test Identify functions

7 2 Algebraic Prerequisites 2 Solve problems involving functions Find the domain and range of a function Find the slope of a line Write equations in the slopeintercept form Find an equation given two points Explain parallel and perpendicular lines Workbook: pp Sections 1.8 to 1.13 Submit Test 1 Graph functions Graph functions with shifts and stretches 3 Algebraic Prerequisites 3 Test functions for symmetry and reflection Explain and use quadratic equations Graph quadratic equations Define and use composite functions Explain and apply rational functions Graph rational functions Find horizontal and vertical asymptotes Workbook: pp Sections 1.14 to 1.20 Submit Test 2 Use the horizontal line test Graph the inverse of functions 4 Find the inverse of a function Trig Functions 1 Course Objective 1 Measure angles Workbook: pp Submit Test 3

8 Classify angles Convert radians to degrees and degrees to radians Evaluate trig functions Identify and use the trig functions of acute angles Sections 2.1 to 2.3 Identify and use the trig functions of special angles Apply trig functions to right triangles. Evaluate trig functions using the reference angle Submit Test 4 5 Trig Functions 2 Course Objective 1 Graph the sine and cosine functions Find the max and min values of sine and cosines Graph the sine and cosine functions with vertical and horizontal shifts Graph the tangent, secant, cosecant and cotangent Workbook: pp Sections 2.4 to 2.7 Identify trig function graphs Evaluate inverse trig Functions 6 Apply trig functions to solve problems. Trig Identities 1 Course Objective 1-2 Identify the fundamental trig identities Simplify trig expressions Workbook: pp Sections 3.1 to 3.4 Submit Test 5

9 Verify trig identities Solve trig equations Submit Test 6 7 Trig Identities 2 Course Objective 1-2 Apply the sums and differences identities Use the double-angle and half angle identities. Apply the product-to sum identity Use the sum-to-product identity Workbook: pp Sections 3.5 to Apply functions of the form f(x) = a sin x + b cos x Trig Applications Course Objective 1-2 Apply the Law of Sines Apply the Law of Cosines Find the area of a triangle Use Heron formula Workbook: pp Sections 4.1 to 4.2 Submit Test 7 Submit Test 8 9 Vectors Course Objective 3 Identify and use vectors to solve problems Find the magnitude and direction of a vector Workbook: pp Sections 4.3 to 4.4

10 Find the components of a vector Solve problems using vectors Submit Test 9 10 Complex Numbers and Polar Coordinates Course Objective 3 Explain complex numbers Add and subtract complex numbers Multiply and divide complex numbers Apply powers of i Explain and find roots using DeMoivre s Theorem Workbook: pp Sections 5.1 to 5.4 Log and Exponentials 1 Convert rectangular coordinates to polar coordinates Course Objective 4 Graph an exponential function Describe and use the natural exponential function Workbook: pp Sections 6.1 to 6.5 Submit Test Graph the logarithmic function Apply the log functions Submit Test Log and Exponentials 2 Course Objective 4 Use the properties of logarithms to solve problems Use the change of base formula Workbook: pp Sections 6.6 to 6.9

11 Use log scales Solve exponential equations Solve log equations Submit Test Log and Exponentials 3 Course Objective 4 Use the properties of exponential functions to solve practical applications Solve exponential equations Solve logarithmic equations Apply exponents and logarithms Workbook: pp Sections 6.10 to 6.11 Submit Test Conic Sections Course Objective 5 Graph and apply parabolas, hyperbolas and ellipses Explain the rotation theorem for conics Identify conic sections using the conic identification theorem. Identify the conic sections Workbook: pp Sections 7.1 to Course review Course Objective 1 5 Review all course material Review the course material and prepare for the final examination Submit Test 14 There is no discussion forum this week. Final Examination Course Objective 1 5 Final required contact be sure to stop by the

12 Demonstrate your knowledge of trigonometry discussion forum for the Final Debriefing Submit Final Examination by 11:55 PM Eastern time, on Sunday. (Covers the material in Weeks 1-14) (20 % of overall grade) Policies Please see the Student Handbook to reference all University policies. Quick links to frequently asked question about policies are listed below. Drop/Withdrawal Policy Plagiarism Policy Extension Process and Policy Disability Accommodations Late Assignments Students are expected to submit classroom assignments by the posted due date and to complete the course according to the published class schedule. As adults, students, and working professionals, I understand you must manage competing demands on your time. Should you need additional time to complete an assignment, please contact me before the due date so we can discuss the situation and determine an acceptable resolution. Routine submission of late assignments is unacceptable and may result in points deducted from your final course grade. Netiquette Online universities promote the advancement of knowledge through positive and constructive debate both inside and outside the classroom. Forums on the Internet, however, can occasionally degenerate into needless insults and flaming. Such activity and the loss of good manners are not acceptable in a university setting basic academic rules of good behavior and proper Netiquette must persist. Remember that you are in a place for the rewards and excitement of learning which does not include descent to personal attacks or student attempts to stifle the Forum of others.

13 Technology Limitations: While you should feel free to explore the full-range of creative composition in your formal papers, keep layouts simple. The Sakai classroom may not fully support MIME or HTML encoded messages, which means that bold face, italics, underlining, and a variety of color-coding or other visual effects will not translate in your messages. Humor Note: Despite the best of intentions, jokes and especially satire can easily get lost or taken seriously. If you feel the need for humor, you may wish to add emoticons to help alert your readers: ;-), : ), Disclaimer Statement Course content may vary from the outline to meet the needs of this particular group. Online Library The Online Library is available to enrolled students and faculty from inside the electronic campus. This is your starting point for access to online books, subscription periodicals, and Web resources that are designed to support your classes and generally not available through search engines on the open Web. In addition, the Online Library provides access to special learning resources, which the University has contracted to assist with your studies. Questions can be directed to Charles Town Library and Inter Library Loan: The University maintains a special library with a limited number of supporting volumes, collection of our professors publication, and services to search and borrow research books and articles from other libraries. Electronic Books: You can use the online library to uncover and download over 50,000 titles, which have been scanned and made available in electronic format. Electronic Journals: The University provides access to over 12,000 journals, which are available in electronic form and only through limited subscription services. Tutor.com: AMU and APU Civilian & Coast Guard students are eligible for 10 free hours of tutoring provided by APUS. Tutor.com connects you with a professional tutor online 24/7 to provide help with assignments, studying, test prep, resume writing, and more. Tutor.com is tutoring the way it was meant to be. You get expert tutoring whenever you need help, and you work one-to-one with your tutor in your online classroom on your specific problem until it is done. The course guide for this course can be found here (

14 The AMU/APU Library Guides provide access to collections of trusted sites on the Open Web and licensed resources on the Deep Web. The following are specially tailored for academic research at APUS: Program Portals contain topical and methodological resources to help launch general research in the degree program. To locate, search by department name, or navigate by school. Course Lib-Guides narrow the focus to relevant resources for the corresponding course. To locate, search by class code (e.g., SOCI111), or class name.

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