# 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.

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.

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

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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