Santa Barbara City College Course Outline

MATH 138 - Precalculus - College Algebra and Trigonometry

MATH 138
Precalculus - College Algebra and Trigonometry
Disciplines
Mathematics (Masters Required)
4.000
0 - May not be repeated
Advanced algebra course emphasizing analysis, graphing and applications of trigonometric functions. Such functions are developed from circular functions. Trigonometric identities and conditional equations, applications to triangles, vectors, complex numbers, parametric equations and polar coordinates are covered. Additional topics include matrix algebra, logic and structure of proof, and the Binomial Theorem.
64.000-72.000 Total Hours
Total Hours
128.000-144.000 Total Hours
64.000-72.000 Total Hours
Prerequisite: MATH 137 or equivalent based on SBCC's Assessment Center placement via multiple measures.
Prerequisite or Corequisite: None
Concurrent Corequisite: None
Course Advisories: None
Limitation on Enrollment: None
Course Objectives:
Describe the behavior of functions needed to start the study of calculus, including exponential and logarithmic functions, and to recognize their corresponding graphs.
Solve advanced algebraic and trigonometric equations.
Use the appropriate trigonometric functions in applications to the physical sciences.
Use trigonometry in simple applications such as triangle solving problems, polar coordinates, parametric equations, and vectors in two dimensions.
Analyze and solve problems involving algebraic fundamentals, functions, graphs, and trigonometric functions.
Apply the logical structure of proofs and work symbolically with connectives and quantifiers to produce logically valid, correct and clear arguments, as well as analyze and critique logical arguments.
Use graphing technology such as graphing calculators and computer software to create graphs, and tables of values for algebraic, trigonometric and transcendental functions.
Student Learning Outcomes
MATH138 SLO1 - Identify the periodic behavior of trigonometric functions, and use properties of trigonometric functions to construct their equations and graphs.
MATH138 SLO2 - Apply different types of trigonometric identities and construct logical arguments involving these identities.
MATH138 SLO3 - Solve trigonometric equations.
MATH138 SLO4 - Apply methods of trigonometry to applications involving triangles, polar coordinates, parametric equations, and vectors in two dimensions.

  1. Trigonometric functions

    1. Sine and cosine functions developed from unit circle

    2. The remaining four trigonometric functions

    3. Angles and trigonometric functions of angles

    4. Radian measure and circular motion

    5. Graphs of trigonometric functions

    6. Inverse trigonometric functions

    7. Trigonometric identities for a single angle

    8. Identities for sums and differences, multiple angle identities

    9. Product identities

    10. Conditional equations

    11. Harmonic motion (optional)

  2. Applications of trigonometry

    1. Right triangles

    2. Oblique triangles

    3. Polar coordinates

    4. Polar form of complex numbers

    5. Demoivre’s theorem

  3. Matrices and Vectors

    1. Vectors and vector operations

    2. Matrices and matrix operations

    3. Applications to linear systems

  4. Logic and Proof

    1. Sets and set operations

    2. Disjunction, conjunction, negation, implication and equivalence

    3. Direct and indirect proofs

    4. Binomial theorem

    5. Induction

  5. Parametric Equations

    1. Sketching parametric curves, including orientation

    2. Parameterizing curves



Methods of Instruction
Directed Study
Discussion
Distance Education
Lecture
Lecture is the primary activity, along with student problem-solving activities. Students are expected to work outside of class on assigned exercises and supplemental reading from the text.
-High tide occurs at 7am and the depth of the water is 16 ft. Low tide occurs at 1pm and the depth of the water is 4 ft. Find the period of the sinusoidal function that gives the depth of the water as a function of time. (Use 0 to correspond with high tide)
A. Appropriate Readings: Students are required to read assigned sections in text or supplements. B. Writing Assignments: Students must work assigned mathematical problems requiring the manipulation of abstract symbols. C. Appropriate Outside Assignments: Students are expected to spend a sufficient amount of time outside of class to practice techniques presented during class time, read assigned materials, and complete frequent homework assignments. D. Appropriate Assignments that Demonstrate Critical Thinking: Students must demonstrate mathematical skills which involve analyzing information, recognizing concepts in new contexts, and drawing analogies. They must also analyze using both inductive and deductive reasoning within a logical system.
A student’s grade will be based upon multiple measures of performance in the solving of algebraic problems, in the preparation and analysis of graphs, and in the analysis of logical arguments. Such measures may include at least four one-hour exams (or equivalent) and a comprehensive final examination requiring demonstrations of problem-solving skills. In addition, instructors may make use of quizzes, written homework assignments, or other appropriate means to judge a student’s dexterity with algebra skills and familiarity with mathematical vocabulary. In accordance with district policy, instructors are to provide students a written course syllabus which will include the specific procedures by which students will be evaluated. These procedures must be consistent with the objectives and course content stated above.
    PrecalculusOpenstax, Openstax, 2014Precalculus: Mathematics for Calculus with WebassignStewart, Cengage, 2018
  • TI-84 Graphing Calculator
09/04/2019
Board of Trustees: 04/09/2020
CAC Approval: 03/30/2020