SANTA BARBARA CITY COLLEGE

ASSOCIATE DEGREE CREDIT COURSE OUTLINE

Department: Mathematics

Subject Area and Course Number: Mathematics 138

Course Title: Precalculus II–College Algebra and Trigonometry

Discipline: Mathematics

Units: 4

Repeatability: None

Catalog Course Description: Advanced algebra course, emphasizing analysis, graphing and applications of trigonometric functions. Such functions are developed from circular functions. Trigonometric identities and conditional equations, as well as applications to triangles, vectors, complex numbers, parametric equations, and polar coordinates. Additional topics include conic sections, sequences, series and the Binomial Theorem.

Description for Schedule of Classes: Extensive treatment of graphing and applications of exponential, logarithmic and trigonometric functions. Vectors, complex numbers, parametric equations, and polar coordinates. Other topics include mathematical induction, sequences, series and Binomial Theorem.

Lecture Hours per Week: 4 (64-72 Total Semester Hours)

Laboratory Hours per Week: None

Plus Hours: None

Prerequisites: Math 137 with a grade of “C” or better or qualifying score on SBCC placement exam.

Co-requisites: None

Skills Advisories: Eligibility for English 100 or English 103

Course Advisories: None

Limitation on Enrollment: None

Course Objectives: At the completion of this course, the student will be able to:

1. Demonstrate the ability to describe the behavior of functions needed to start the study of calculus, including exponential and logarithmic functions, and to recognize their corresponding graphs.

2. Demonstrate refined skills in algebraic manipulations and equation solving.

3. Demonstrate the understanding of the trigonometric functions appropriate for the study of calculus and for applications to the physical sciences.

4. Use trigonometry in simple applications such as triangle solving problems.

5. Analyze and solve problems involving algebraic fundamentals, functions, graphs, and trigonometric functions.

6. Demonstrate a familiarity with mathematical reasoning and be able to analyze and critique logical arguments.

7. Demonstrate a basic understanding of sequences, series, and the binomial theorem.

8. Use graphing technology such as graphing calculators and computer software to create graphs, and tables of values for algebraic, trigonometric and transcendental functions.

Course Content and Scope:

1. Trigonometric Functions

a. Sine and cosine functions developed from the unit circle

b. The remaining four trigonometric functions

c. Angles and trigonometric functions of angles

d. Radian measure and circular motion

e. Graphs of trigonometric functions

f. Inverse trigonometric functions

g. Trigonometric identities for a single angle

h. Identities for sums and differences – multiple angle identities

i. Product Identities

j. Conditional equations

k. Harmonic motion (optional)

2. Applications of trigonometry

a. Right triangles

b. Oblique triangles – law of sines and law of cosines

c. Vectors

d. Polar coordinates

3. Introduction to discrete mathematics

a. Binomial Theorem

b. Sequences and series – notation

c. Mathematical induction

d. Trigonometric form of complex numbers and DeMoivre’s Theorem

4. Conic Sections

a. Geometric description of the three types of conic sections

b. Equations and graphs of rectangular conic sections

Methods of Instruction: 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.

Required Assignments:

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.

Methods of Evaluation: 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 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.

Appropriate Texts and Supplies:

Cohen, Precalculus with Unit-Circle Trigonometry, 4^th Ed., Cengage Publishing, 2006

TI-84 Graphing Calculator

Student Learning Outcomes:

1. Distinguish among different types of conic sections; construct graphs of conic sections from their equations, and vice versa.

2. Identify the periodic behavior of trigonometric functions, and use properties of trigonometric functions to construct their equations and graphs.

3. Apply different types of trigonometric identities and construct logical arguments involving these identities.

4. Solve trigonometric equations.

5. Apply methods of trigonometry to applications involving triangles and vectors in two dimensions.

IA/mej/ FRC (WPC)

Revised August 2006; 8/24/09