KERN COMMUNITY COLLEGE DISTRICT – CERRO COSO COLLEGE

MATH C142 COURSE OUTLINE OF RECORD

  1. DISCIPLINE AND COURSE NUMBER:
    MATH C142
  2. COURSE TITLE:
    Trigonometry
  3. SHORT BANWEB TITLE:
    Trig
  4. COURSE AUTHOR:
    Bernsten, Dean
  5. COURSE SEATS:
    -
  6. COURSE TERMS:
    30 = Spring; 50 = Summer
  7. CROSS-LISTED COURSES:
  8. PROPOSAL TYPE:
    CC Course Revision
  9. START TERM:
    30 = Spring, 2012
  10. C-ID:
  11. CATALOG COURSE DESCRIPTION:
    Trigonometry is an intensive study of trigonometric and inverse trigonometric functions, the graphical representations of these functions, solving trigonometric equations, verifying identities, solving triangles in the plane and on the sphere, complex numbers and De Moivre''s theorem. Topics in analytic geometry in two and three dimensions, such as polar coordinates and vectors, and their applications are also covered. A symbolic manipulation processor or a graphing calculator is strongly recommended.

  12. GRADING METHOD

    Default:
    S = Standard Letter Grade
    Optional:
    A = Audit;P = Pass/No Pass
  13. TOTAL UNITS:
    4

  14. INSTRUCTIONAL METHODS / UNITS & HOURS:

    Method
    Min Units
    Min Hours
    Lecture
    4
    72
    Lab
    0
    0
    Activity
    0
    0
    Open Entry/Open Exit
    0
    0
    Volunteer Work Experience
    0
    0
    Paid Work Experience
    0
    0
    Non Standard
    0
    0
    Non-Standard Hours Justification:

  15. REPEATABILITY

    Type:
    Non-Repeatable Credit
  16. MATERIALS FEE:
    No
  17. CREDIT BY EXAM:
    No
  18. CORE MISSION APPLICABILITY:
    Associate Degree Applicable (AA/AS);Certificate of Achievement (COA);CSU Transfer;Career Technical Education (CTE)
  19. STAND-ALONE:
    No

  20. PROGRAM APPLICABILITY

    Required:
    Engineering Technology (AS Degree Program)
    Engineering Technology AS (AS Degree Program)
    Engineering Technology Cert (Certificate of Achievement)
    Engineering Technology- (Certificate of Achievement)
    Elective:
    General Education ()
    Liberal Arts: Mathematics & Science (AA Degree Program)

  21. GENERAL EDUCATION APPLICABILITY

    Local:
    CC GE Area IV: Language and Rationality = Analytical Thinking;
    IGETC:
    CSU:
    CSU GE Area B: Physical and its Life Forms(mark all that apply) = B4 - Mathematics/Quantitative Thinking;
    UC Transfer Course:
    CSU Transfer Course:

  22. STUDENT LEARNING OUTCOMES Upon completion of the course, the student will be able to

    1. Interrelate the multiple definitions of the trigonometric functions and their inverses.
    2. Determine the appropriate trigonometric ratio or law to apply to solve problems with triangles.
    3. Use the radian measure effectively in conversions and in applying formulas to solve problems.
    4. Analyze trigonometric functions and their graphs using the concepts of amplitude, period, phase and vertical shifts and apply these ideas to real-world problems.
    5. Recognize and verify or prove trigonometric identities.
    6. Analyze trigonometric equations to determine what combination of algebra and identities will lead to a solution.
    7. Apply trigonometry to operations with complex numbers.
    8. Solve problems and graph equations of conic sections in rectangular and polar coordinate systems in two and three dimensions.
    9. Identify and solve problems using parametric equations and vectors in the plane and in space.

  23. REQUISITES

    Prerequisite:

    MATH C055

  24. DETAILED TOPICAL OUTLINE:

    Lecture:

    The Mathematics Department has adopted the following best practices for teaching this course:  offering or awarding extra-credit is forbidden, the allowance of multiple attempts at exams is forbidden, and an approved on-site proctor for online course exams is required.

    A.   The Trigonometric Functions

    1.     Review of rectangular coordinate system and the Pythagorean Theorem.

    2.     Standard position for angles, positive, negative, and coterminal angles.

    3.     Definitions of the six trigonometric functions using x, y, and r and proof of the values for the quadrantal angles.

    4.     Reciprocal identities, function sizes, and signs in the quadrants.

    B.    Acute Angles and Right Triangles

    1.     Definitions of the trigonometric identities using side opposite, side adjacent, and hypotenuse, and introduction of cofunctions

    2.     Trigonometric values based on the 30-60-90 and 45-45-90 reference triangles

    3.     Reference angles and their uses

    4.     Solving right triangles

    5.     Applications of right triangles, including angle of elevation, angle of depression, and bearing

    C.    Radian Measure and Circular Functions

    1.     Conversions between degrees and radian measure systems

    2.     Length of arc and area of sector

    3.     Definition of the circular functions and the use of tables

    4.     Linear and angular velocity

    D.    Graphs of the Trigonometric Functions

    1.     Graphs of sine and cosine, with variations in period and amplitude

    2.     Graphs of tangent, cotangent, secant, and cosecant

    3.     Vertical shifts and phase shifts

    4.     Graphing by addition of ordinates

    5.     Applications of graphs of sinusoids

    E.    Trigonometric Identities

    1.     Reciprocals, quotients, Pythagorean identities, negative angles

    2.     Verifying and simplifying trigonometric identities

    3.     Sum and difference identities for sine, cosine, and tangent

    4.     Double, half-angle, and power-reducing identities

    5.     Sum and product identities

    F.     Inverse Trigonometric Functions

    1.     Review of inverse functions

    2.     Defining the inverse trigonometric functions

    3.     Methods of solving trigonometric equations

    4.     Solving trigonometric equations with multiple angles

    5.     Solving Inverse trigonometric equations

     

    G.    Triangles and Vectors

    1.     Law of Sines, including the ambiguous case

    2.     Law of Cosines

    3.     Vector addition, subtraction, scalar multiplication

    4.     Applications of vectors

    H.    Complex Numbers

    1.     Review of properties of complex numbers

    2.     Writing complex numbers in standard form and in trigonometric form

    3.     Multiplication and division in trigonometric form

    4.     De Moivre's Theorem

    5.     Nth roots of a complex number

    I.     Polar Coordinates and Parametric Equations

    1.     Plotting points in the polar coordinate system

    2      Polar equations and their graphs

    3.     Using trigonometric functions in parametric equations

    J.     Additional Topics in Analytic Geometry - Conic Sections

    1.     Parabolas

    2.     Ellipses

    3.     Hyperbolas

    4.     Rotations and Systems of Quadratic Equations

    K.    Analytic Geometry in Three Dimensions

    1.     The Three-Dimensional Coordinate System

    2.     Vectors in Space

    3.     The Cross Product of Two Vectors

    4.     Lines and Planes in Space

    L.    Selected Trigonometric Applications to Be Chosen From

    1.     Mathematics: other branches

    2.     Biological Sciences: e.g. general biology, anatomy, physiology, microbiology

    3.     Physical Sciences: e.g. chemistry, physics, geology, astronomy, oceanography

    4.     Computer Science: e.g. computer graphics, computer animation

    5.     Music

  25. METHODS OF INSTRUCTION--Course instructional methods may include but are not limited to

    1. Discussion;
    2. Lecture;
    3. Other Methods: A. Textbook readings B. Lectures C. Online course management system D. Discussions

  26. OUT OF CLASS ASSIGNMENTS: Out of class assignments may include but are not limited to

    A. Daily homework assignments Example: Students work mathematics problems assigned from the text and from hand-outs to reinforce concepts and skills discussed in lecture. B. Online Course Management System Example: Assignments on CourseCompass

  27. METHODS OF EVALUATION: Assessment of student performance may include but is not limited to

    A. Daily in-class assignments
    Example: Students work mathematics problems assigned from the text and from hand-outs to reinforce concepts and skills discussed in lecture.
    B. Weekly Quizzes
    Weekly quizzes over the previous week’s lecture material, homework, and in-class assignments assess the student’s understanding.
    C. Chapter Exams
    Chapter exams over the previous chapter’s lecture material, homework, and in-class assignments assess the student’s understanding.

  28. TEXTS, READINGS, AND MATERIALS: Instructional materials may include but are not limited to

    Textbooks
    Sullivan, M.. (2012) Precalculus, 9th, Prentice Hall Publishing Company
    Manuals
    Periodicals
    Software
    Other
  29. METHOD OF DELIVERY:
    Online with some required face-to-face meetings (“Hybrid”);iTV – Interactive video = Face to face course with significant required activities in a distance modality ;Online course with on ground testing;Face to face;
  30. MINIMUM QUALIFICATIONS:
    Chemistry (Masters Required);Engineering (Masters Required);Mathematics (Masters Required);Physics/Astronomy (Masters Required);

  31. APPROVALS:

    Origination Date
    10/28/2011
    Last Outline Revision
    02/24/2012
    Curriculum Committee Approval
    02/24/2012
    Board of Trustees
    05/03/2012
    State Approval
    UC Approval
    UC Approval Status
    CSU Approval
    50 = Summer 2000
    CSU Approval Status
    Approved
    IGETC Approval
    IGETC Approval Status
    CSU GE Approval
    50 = Summer 2000
    CSU GE Approval Status
    Approved