Course Title:
| Trigonometry and Analytical Geometry | |
Course Materials:
Aufmann, R. N., Barker, V. C., & Nation, R. D. (2008). College algebra and trigonometry (6th ed.). Boston: Houghton Mifflin Company.
Scientific Calculator required.
Student's solution manual - DE required.
An equation editor - DE required. | |
Course Description:
| MATH 108 Trigonometry and Analytical Geometry (3) (The second course in the two-course series MATH 107-108. An alternative to MATH 115 Pre-Calculus.) Prerequisite: MATH 107 or an appropriate result on the placement test. An introduction to trigonometric functions, identities, and equations and their applications. Analytical geometry and conic sections are covered. Additional topics may include matrices, determinants, sequences, and series. Students may receive credit for only one of the following courses: MATH 108 or MATH 115. | |
Course Goals/Objectives:
Upon successful completion of this course, minimal objectives the student has achieved include the following:
* Convert between decimal degree measure, degree-minute-second measure, and radian measure;
* Find the values for the six trigonometric functions of any acute angle of a right triangle, of any angle in standard position, and of real numbers;
* Graph the trigonometric functions, translations, and inverses of those graphs;
* Verify trigonometric identities, and solve trigonometric equations;
* Evaluate a trigonometric expression that contains the inverse of trigonometric functions;
* Solve applied problems involving the use of right triangles and the trigonometric functions;
* Perform simple manipulations in vector algebra.
* Write a complex number in trigonometric form and in standard form, and find the product, quotient, and the power of a complex number written in trigonometric form;
* Construct detailed graphs of the conic sections;
Additional objectives may include:
* Transform equations between the polar coordinate system and the rectangular coordinate system and sketch the graph.
* solve systems of equations using matrices and determinants;
* classify a sequence or a series as arithmetic or geometric, and find terms of a sequence and evaluate series;
* prove a formula using mathematical induction. | |
Course Introduction:
| Math 108 is designed primarily to prepare students for baccalaureate degree programs in engineering, the physical sciences, computer science and mathematics. MATH 108 is the second half of a pre-calculus sequence, stressing problem-solving rather than theorem-proving methods. The course covers trigonometry, some analytic geometry and a few other topics in preparation for the calculus series, Math 130,131, and 132 or Math 140,141. Modern applications of trigonometry include sound, light and electrical waves, business cycles, and planetary motion. This course provides foundations for lifelong skills in quantitative reasoning. | |
Grading Information and Criteria:
There will be three 75-minute exams each worth 15% of the final grade and a comprehensive final exam that is worth 40% of the final grade. The remaining 15% of the final course grade will be comprised of optional projects, quizzes, or homework assignments.
Assessment Item
Points
% of Final Grade
Exam 1
15 points
15
Exam 2
15 points
15
Exam 3
15 points
15
Projects/Quizzes/
Homework Assignments
15 points
15
Final Exam
40 points
40
Grades will be determined by the number of points you have earned as follows:
Grade
Points
A
90-100
B
80-89.9
C
70-79.9
D
60-69.9
F
<60
NOTE: Faculty may edit this model. Participation as a component is advisable for online classes and may be incorporated in f2f classes. If the faculty wishes to incorporate participation as part of the course grade, then the above percentages will change. Assignment of projects is optional. | |
Other Information:
* Study time (including reading and exercises) can be expected to be 2 to 3 times the amount of lecture time. That is, for every hour in class expect to spend 2 to 3 hours out of class studying.
* Students who fall behind or fail to attempt the exercises could well find themselves in difficulty. Try to incorporate the skills and methods learned in this course in everyday life. It is the best way to learn.
* Attendance: It will be to the student's advantage to attend all classes. When absence is unavoidable, it is a student's own responsibility to makeup any work missed before the next class session. For administrative purposes, attendance will be recorded. Students expecting or experiencing long absences during the term should contact the faculty.
* Class Discussions: Students are encouraged (indeed, expected) to participate. Ask questions.
* Homework assignments will be given for each class session. You are responsible for solving all problems assigned. Completing all the homework problems should help you prepare for the exams. If there are any problems that you found difficult or were unable to solve, be prepared to ask questions concerning those problems. Mastery of math depends on practice, practice, practice!
* In addition to the textbook, you will need a scientific calculator and graph paper with grid size large enough to see without the aid of a magnifying glass. A straight edge and a few different colored pencils or pens may also be useful.
* Please do not tape record class sessions.
* Please turn off telephones before class. | |
Project Descriptions:
| If the faculty member incorporates projects as part of the course grade, the problems comprising the projects might come from the Topics for Discussion/Projects that are a part of each section of the textbook or the faculty member might create projects based upon current events or items that are useful and of interest to the class. | |
Academic Policies:
Cases of plagiarism are handled consistent with current UMUC guidelines.
See the UMUC policies at the following URL:
http://www.umuc.edu/policy/ | |
Course Schedule:
Tentative Schedule; may be modified by instructor as circumstances deem necessary. All readings and assignments are from College Algebra and Trigonometry, by Aufman, Baker and Nation. Please read the sections to be covered prior to the class meeting. Homework assignments will be comprised of the odd numbered problems in each section unless specified otherwise during the class meetings.
Class Sections, Meeting, Covered Topics, and Exams
1 5.1-5.3 Trigonometric Functions of Angles
2 5.4, 5.5 Trigonometric Functions of Real Numbers, Graphs
3 5.6-5.8 Graphing
4 6.1, 6.2 Trigonometric Identities
5 6.3, 6.4 Exam I, Trigonometric Identities
6 6.5, 6.6 Inverse Trigonometric Functions, Trigonometric Equations
7 7.1, 7.2 Laws of Sines and Cosines
8 7.3-7.5 Vectors, Complex Numbers
9 8.5 Exam II, Polar Coordinates
10 8.1-8.4 Conic Sections
11 8.6-9.2 Polar Equations of the Conics, Parametric Equations, Systems of Linear Equations
12 10.1,10.4,10.5 Matrices and Determinants
13 9.3-9.5 Exam III, Systems of Equations and Inequalities, Partial Fractions
14 11.1-11.3 Sequences and Series
15 11.4, 11.5 Mathematical Induction, Review for Final
16 Final Exam
NOTE: Exam I covers 5.1-6.2
Exam II covers 6.3-7.5
Exam III covers 8.1-9.2, 10.1, 10.4, and 10.5
Final Exam is comprehensive | |
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