MATH122 Trigonometry and Analytic Geometry

Department of Science, Technology, Engineering & Mathematics: Mathematics

I. Course Number and Title
MATH122 Trigonometry and Analytic Geometry
II. Number of Credits
3 credits
III. Minimum Number of Instructional Minutes Per Semester
2250 minutes
IV. Prerequisites
Math Placement Test score of 8 or better or MATH120 (C or better)
V. Other Pertinent Information
A comprehensive departmental final examination is included in the course.
VI. Catalog Course Description
Topics in this course includes right triangle trigonometry, trigonometric functions and their inverses, identities, equations, solutions of oblique triangles, complex numbers, and analytic geometry.
VII. Required Course Content and Direction
  1. Learning Goals:

    Course Specific:
    The student will be able to:
    1. develop an understanding of trigonometric functions and the skill of graphing these periodic functions.
    2. develop a proficiency in the use of the unit circle to find exact values of trigonometric expressions.
    3. develop the skill of using a graphing calculator for trigonometric computations, graphing trigonometric functions, and finding values for inverse trigonometric ratio functions.
    4. demonstrate an understanding of the concept of conic sections and develop the skill of deriving the equations and graphing the equations of conic sections.

    Core Learning Goals:
    Category I:
    Math or Science:
    The students will be able to:
    1. develop the ability to analyze, interpret, and apply quantitative information.

    Core Learning Objectives:
    Category I:
    Math or Science:
    The students will be able to:
    1. accurately translate descriptive problems into mathematical formulas and solve them. (1)

    Category III:
    Critical Thinking/Problem Solving:
    The students will be able to:
    1. demonstrate an understanding of solving problems by:
      1. recognizing the problem
      2. reviewing information about the problem
      3. developing plausible solutions
      4. evaluating the results
  2. Planned Sequence of Topics and/or Learning Activities:

    The following is a list of the minimum amount of course material to be covered by the instructor. Accompanying each topic is an approximate number of lessons required to study the topic.

    1. Trigonometric Functions (8 lessons)
      1. Angle Measurement (degree and radian measure)
      2. Angle Relationships and Similar Triangles
      3. Definitions of Trigonometric Functions
      4. Trigonometric Functions of Acute and Non-Acute Angles

    2. Right Triangle Trigonometry (4 lessons)
      1. Solving Right Triangles
      2. Applications

    3. Circular Functions (5 lessons)
      1. Circular Functions of Real Numbers
      2. Linear and Angular Velocity
      3. Graphs of the Basic Trigonometric Functions
      4. Vertical and Horizontal Translations of Basic Graphs

    4. Identities (6 lessons)
      1. Pythagorean and Reciprocal Identities
      2. Sum and Difference Identities
      3. Half and Double Angle Identities
      4. Verifying Identities

    5. Inverse Functions (3 lessons)
      1. Definitions and Graphs of Inverse Functions
      2. Solving Equations

    6. Solving Oblique Triangles (4 lessons)
      1. Law of Sines
      2. Law of Cosines
      3. Area Formulas
      4. Applications

    7. Vectors (2 lessons)
      1. Magnitude and Direction Angle
      2. Addition, Subtraction, and Scalar Multiplication
      3. Dot Product
      4. Applications

    8. Complex Numbers (2 lessons)
      1. Trigonometric and Rectangular Form
      2. Multiplication and Division
      3. Powers and Roots of Complex Numbers

    9. Polar Equations and Graphs (1 lesson)

    10. Parametric Equations and Graphs (1 lesson)

    11. Analytic Geometry (3 lessons)
      1. Parabola
      2. Ellipse
      3. Hyperbola
  3. Assessment Methods for Core Learning Goals:

    All Core Critical Thinking and Problem Solving, College Level Mathematics or Science, and Discipline-Specific Course Objectives will be assessed as follows:

    The student will apply mathematical concepts and principles to identify and solve problems presented through informal assessment, such as oral communication among students and between teacher and students and, for the core, formal assessment using open-ended questions reflecting theoretical and applied situations.

  4. Reference, Resource, or Learning Materials to be used by Students:

    Departmentally selected textbook. Details provided by the instructor of each course section. See Course Format.
VIII. Teaching Methods Employed
Primary teaching methods are lecture, recitation, problem solving, and class discussion as appropriate.

Review/Approval Date - 3/06; Core Goals/Objectives added 5/04