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MAT 145

I.   TITLE:  Trigonometry

II.   CATALOG DESCRIPTION:  Plane Trigonometry.  Restriction: A student may not receive credit for MAT 145 and MAT 130 or 150.  (MAT 145 in combination with MAT 140 will substitute for MAT 150.)

III. PURPOSE:  Trigonometry has been used for millennia to solve a variety of problems, ranging from astronomy to construction.  As such, students taking this course will be exposed to some of the classical problems of science, with the consideration of these problems requiring mature thought, analysis and reasoning.  The thought process that students experience often has a pictorial or graphical nature and thus many problems will be explained using either a historically classic drawing or a modern computer image.  The analysis done in this course provides the students with both a graphical understanding as well as numerical intuition with regard to basic problems in engineering and design.  The material in this course plays an important role in the educational foundation on which students will construct a mastery of their chosen field.

IV.  COURSE OBJECTIVES:
1.   Fundamental Concepts:
The student should gain a solid understanding of the use of  trigonometry and applications.  The course begins with fundamental  properties of angles and triangles and extends through vectors and  complex number representations.  Students should:
  a.   understand the trigonometry of the right triangle,
  b.  understand the measure of angles using degrees and     radians,
  c.   understand the extension of right triangle trigonometry     to the circular functions,
  d.  know the properties of the circular functions,
  e.  understand the trigonometric description of vectors, and
  f. know the trigonometric description of complex numbers.
2.   Application of Content: In this course the student will see a connection to society through:
  a.   applications of trigonometry to problems of astronomy,
  b. applications of trigonometry to problems related to      highway construction,
  c. applications of trigonometry to problems related to the     movement of the earth relative to the sun,
  d. applications of periodic functions to weather prediction,
  e. applications of trigonometric identities to the study of electricity, and
  f. use of graphing calculators to illustrate the notion of     periodicity.
3.   International Perspective:
An understanding of trigonometry and its applications is one  component of a well rounded education, worldwide.  Taught in the  universal language of mathematics, a basic understanding of  trigonometry will enable students to more easily communicate in the  international scientific and economic community.  In addition,  students get an international perspective when the history of  trigonometry is discussed.

V.   CONTENT OUTLINE:
1.   Review of College Algebra
2. Trigonometric functions
3. Acute angles and right triangles
4. Radian measure and circular functions
5. Graphing
  a.  Sine and cosine
  b. Translate of graphs
  c. Other circular functions
6. Trigonometric identities
  a. Fundamental identities
  b. Verifying identities
  c. Other identities
7. Inverse trig functions
8. Applications of trigonometry and vectors
9. Complex numbers and polar form

VI. INSTRUCTIONAL ACTIVITIES:
1. Active learning: This course, of late, has been taught using a cooperative learning  approach.  In a typical class meeting, the instructor gives a written  summary of the material to be covered and lectures briefly at the  start of class. The class then breaks into groups, first discussing the  current material and then working assigned problems. These  problems are then presented by individuals to the rest of the class.   The oral reports typically contribute little quantitatively to the final  grade, but are useful in developing the students' communication and  writing skills.  The instructor circulates throughout the room, giving  assistance and asking questions. A neatly written solution to more  challenging problems is submitted by the group to be graded.   Depending on the instructor, approximately 2 group projects are  submitted,  and approximately 5 problems are presented by each  student.  Students are required to do mathematical writing both for  in class group activities and out of class home work.

2. Critical Thinking: Each student has two daily  responsibilities; to work or finish working problems presented the  previous day and to read the upcoming day's  material.  In order to  successfully accomplish these responsibilities, it is vital that the  student reflect on the material, separating the information into two  primary categories:   material which is propositional in nature and  that which is exemplary or supportive.  Through critical thought,  the student comprehends the meaning and usefulness of stated  propositions by analyzing the supporting examples and digesting  their accompanying proofs or justifications.  The evaluation of  students' ability to think in this manner is made through students'  demonstrations of dexterity with the material as exhibited on exams  and quizzes.

3.   Use of Technology: Each student is required to have a graphing calculator for the class. The calculator is used extensively in graphing  circular functions, verifying identities, examining vectors and  plotting complex numbers.

VII.  FIELD AND CLINICAL EXPERIENCES:  None.

VIII.  RESOURCES: In addition to the text, graphing calculator, and instructor prepared hand-outs, each instructor provides at least 12 scheduled office hours per week.  Tutoring is also available through the Learning Center.  Through collaborative projects and assignments, students are also encouraged to use their peers as a resource.

IX. GRADING PROCEDURES: Final grades are based on exams, homework, quizzes and projects. The number and weight of these vary from instructor to instructor.  Usually three to five in-class exams, accounting for 40-60% of the final grade,  and a comprehensive final  exam worth 15-30% of the grade,  are given.  Homework and reading assignments are made each class period from the text.  Quizzes and/or in-class group projects often contribute 10-30% to the final grade.  On exams and in daily homework, students are asked to demonstrate skills basic to success in future mathematics and science courses and to show a comprehensive knowledge of trigonometric  concepts.  On projects, students are asked to apply the skills they have developed in this course to more complicated problems.  These problems often require analytical thinking beyond what is required on exams.  Final grades are assigned as follows (this may vary  slightly from instructor to instructor):
    90-100 %    A
    80-  89 %    B
    70-  79 %    C
    60-  69 %    D
      0-  59 %    E

X.  ATTENDANCE POLICY:  The student is responsible for all material presented in class, including announcements about course procedures.   Attendance is recorded.  Exams, quizzes, and homework often include questions on material presented only in class, so performance on these reflects attendance.  In addition, there may be assignments and quizzes completed in class.  No make-ups for these are given.

XI.  ACADEMIC HONESTY POLICY:  Any instance of academic dishonesty, as determined by the instructor (in compliance with Board of Regents policy in Academic integrity - Feb. 1975) will result in zero points for the assignment or a course grade of E.

XII. TEXT:  Current

XIII. PREREQUISITES:  ACT math standard score of at least 20 or consent of instructor.

Last updated February 14, 2000. Designed and maintained by Kyosung Koo