MATH 144 Generic Syllabus

Department of Mathematics Generic Syllabus
Boise State University Updated August 23, 2007
MATH 144
Analytic Trigonometry
2 semester credits

Catalog Description

MATH 144 ANALYTIC TRIGONOMETRY (2-0-2). Right-triangle and circular-function approaches to trigonometry. Trigonometric Identities. Graphs of trigonometric functions; amplitude, frequency, phase shift. Inverse trigonometric functions and their graphs. Polar coordinates, polar representation of complex numbers. Credit cannot be granted for both MATH 144 and MATH 147. PREREQ: MATH 143 or satisfactory placement score.

Prerequisites

MATH 143, with a grade of "C" or better; or sufficient score on COMPASS placement exam; or a 93rd -percentile score on the ACT or SAT. The rationale for these prerequisite is to ensure that students have an adequate level of "mathematical maturity" as well as specific background knowledge.

Jurisdiction

This course is controlled by a departmental committee, whose members may or may not be teaching the course. All sections use the same text, which is chosen by the committee. The committee also writes a syllabus detailing which sections should be covered and how much time should be allotted to each. Exams, homework, and grading system are left to the instructor.

Objectives

The objectives of MATH 144 reflect all four of the Department's teaching goals:
  1. Appreciation of mathematical patterns:
    MATH 144 presents several mathematical patterns:
    1. elementary proof patterns;
    2. an almost-axiomatic pattern of trigonometry;
    3. elementary duality patterns such as function inverses and the great geometry-algebra pattern;
    4. elaboration of the Pythagorean pattern to circular trigonometry.
  2. Awareness of applications:
    MATH 144 presents trigonometric applications such as surveying and circular or oscillatory motion while laying groundwork for study of further applications in subsequent courses.
  3. Mastery of some mathematical tools:
    1. geometric effects of algebraic transformations;
    2. algebraic effects of geometric transformations;
    3. algebraic address of trigonometric phenomena;
    4. use of "appropriate technology" to investigate problems.
  4. Mathematics as a language:
    1. algebraic language and its geometric consequences;
    2. geometric language and its algebraic consequences;
    3. grammar of communication with computers and calculators.
Upon completion of this course, students should:
  1. Be able to use the concepts of function, relation, and graphs.
  2. Be able to use the algebraic and geometric language of mathematics correctly and effectively.
  3. Have skill with manipulative trigonometric algebra.
  4. Particular trigonometric knowledge and skills:
    1. a working knowedge of right-triangle trigonometry and the trigonometric functions in this setting: sin, cos, tan, arcsin, arccos, and arctan.
    2. a working knowedge of the unit-circle
      1. circle geometry: tangent lines, arc length, radian measure.
      2. trigonometry and the circular functions in this setting: sin, cos, tan, arcsin, arccos, and arctan. This includes the famous "by-heart" values of the functions: at 30° 45°, 60°, 90°, 120°, 315°, -540° and their radian-measure versions.
    3. a working knowledge of trigonometric graphs: sinusoids, tan, sec, and the inverse-trigonometric graphs.
    4. a working knowledge of the basic identities: the Pythagorean identities, the sum formulas and the multiple-angle formulas.
    5. skill at writing proofs of trigonometric or logarithmic identities.
    6. skill at solving trigonometric equations and the use of graphs or symmetry to find all their solutions.
  5. Have skill in translating problems to relevant prose, graphical, diagrammatic, or algebraic form.
  6. Exhibit a working understanding of reflection, symmetry, and translation of graphs.
  7. Be able to solve "routine" problems efficiently and have at-least-occasional success with more challenging problems.
  8. Be able to cope with the problems inherent in solving elementary trigonometric equations.
  9. Be able to avoid calculator-generated gaffes. Although MATH 144 does not teach calculator or computer skills as an alternative to algebraic techniques, it does bear some responsibility to study use of powerful graphing and algebraic calculators and attendant pitfalls.

Assessment of Learning Objectives

These objectives are periodically assessed via input from client departments and from instructors in MATH 144, MATH 147 and subsequent courses. Although the objectives have not changed in many years, their realization has changed over the time in response to learning research and technological progress.

Assessment of Student Progress

Students will be assessed by evaluating their ability to do problems based on the learning objectives. The problems will occur in several contexts:

Topics and Approximate Timeline

The following table is based on a typical semester schedule- 30 class meetings of 50 minutes each. The actual amount of time spent on each topic will vary slightly from semester to semester and instructor to instructor.
Number of
Topic Meetings
Trigonometric Functions of Angles 7
Trigonometric Functions of Real Numbers 7
Additional Topics in Trigonometry 12
Exams/Review 4

Text

As of fall, 2007, Precalculus, 5th edition, Stewart (Brooks/Cole) and Graphing Calculator Manual with Exercises, Kenny, (Brooks/Cole website).

Format, Student Activities, and Grades

Class meetings involve a combination of lecture, questions and discussion, and sometimes small group activity; the instructor chooses the appropriate mix.
Homework is an important part of the course: the students are striving both for manipulative skill as well as habits of thought. This requires practice.
The instructor chooses the exact grading scheme, but a typical distribution would be:
Homework 10%
3 Exams 65%
Final Exam 25%
Total 100%
Letter grades are usually based on a standard scale in which 90% of the total possible points guarantees an A , 80% a B, and 70% a C, with the instructor having the discretion to raise or lower these cut-offs if warranted.
Using the plus/minus system, one may further refine grades within these cutoffs, but should not expand the grade ranges. For example, if a C is normally 70 - 79, then the C- should not be lower than 70.


File translated from TEX by TTH, version 3.66.
On 23 Aug 2007, 10:09.