Discipline: Mathematics
Originator: Ernesto Reyes
Riverside Community College District
Integrated Course Outline of Record
Mathematics
23
MAT23 : Trigonometry & Precalculus 
College:
Lecture Hours:
90.000 Lab Hours: 54.000 OutsideofClass Hours: 180.000 Units: 6.00 Grading Methods: Pass/No Pass Letter Grade 
Course Description
Prerequisite:
MAT35 or qualifying placement level.
Course Credit Recommendation:
Degree Credit
An accelerated college level math course designed to prepare students for calculus. Students will study polynomial, absolute value, radical, rational, exponential, and logarithmic functions, analytic geometry, and polar coordinates. The study of trigonometric functions, their inverses and their graphs, identities and proofs related to trigonometric expressions, trigonometric equations, solving right triangles, solving triangles using the Law of Cosines and the Law of Sines, and an introduction to vectors. Students who receive credit for MAT 23 cannot receive credit for MAT 10 and MAT 36. 90 hours lecture and 54 hours laboratory. (Letter Grade or Pass/No Pass option.)
Short Description for Class Schedule
An accelerated college level math course designed to prepare students for calculus.
Entrance Skills:
Before entering the course, students should be able to demonstrate the following skills:
Apply the basic operations of algebra on the set of real and complex numbers, polynomials, rational and radical expressions
 MAT35  Simplify algebraic expressions using correct mathematical symbols and language.

Solve linear, rational, quadratic, exponential, radical, logarithmic, and absolute value equations.
 MAT35  Identify and apply appropriate methods to solve rational, radical, exponential, and logarithmic equations.

Solve inequalities and systems of equations.
 MAT35  Simplify algebraic expressions using correct mathematical symbols and language.
 MAT35  Simplify algebraic expressions using correct mathematical symbols and language.

Graph basic functions.
 MAT35  Graph linear and basic nonlinear functions.

Apply basic operations on functions.
 MAT35  Simplify algebraic expressions using correct mathematical symbols and language.
Course Objectives:
Upon successful completion of the course, students should be able to demonstrate the following activities: Graph functions, relations, and polar equations in rectangular coordinates and polar coordinates.
 Synthesize results from the graphs and/or equations of functions and relations.
 Apply transformations to the graphs of functions and relations.
 Recognize the relationship between functions and their inverses graphically and algebraically.
 Solve systems of equations and inequalities.
 Apply functions to model real world applications.
 Identify special triangles and their related angle and side measures.
 Evaluate the trigonometric function of an angle given in degree and radian measure.
 Manipulate and simplify a trigonometric expression.
 Solve trigonometric equations, triangles, and applications.
 Graph the basic trigonometric functions and apply changes in period, phase shift and amplitude to generate new graphs.
 Prove trigonometric identities.
 Solve and apply equations including rational, linear, polynomial, exponential, absolute value, radical, and logarithmic.
 Solve linear, nonlinear and absolute value inequalities.
 Graph the basic trigonometric functions and apply changes in period, phase shift and amplitude to generate new graphs.
 Evaluate and graph inverse trigonometric functions.
 Convert between polar and rectangular coordinates.
 Calculate powers and roots of complex numbers using DeMoivre's Theorem.
 Introduction to vectors.
 Solve applications involving the Pythagorean theorem and special right triangles.
 Solve applications involving angles and a transversal.
 Solve applications involving the distance formula.
 Solve applications involving similar triangles.
 Find the area and volume of geometric shapes.
Student Learning Outcomes:
Upon successful completion of the course, students should be able to demonstrate the following skills: Solve algebraic, exponential, logarithmic, and trigonometric equations and algebraic inequalities using appropriate techniques.
 Critical Thinking: Students will be able to demonstrate higherorder thinking skills about issues, problems, and explanations for which multiple solutions are possible. Students will be able to explore problems and, where possible, solve them. Students will be able to develop, test, and evaluate rival hypotheses. Students will be able to construct sound arguments and evaluate the arguments of others.
 Graph algebraic, exponential, logarithmic and trigonometric functions.
 Communication Skills: Students will be able to communicate effectively in diverse situations. They will be able to create, express, and interpret meaning in oral, visual, and written forms. They will also be able to demonstrate quantitative literacy and the ability to use graphical, symbolic, and numerical methods to analyze, organize, and interpret data.
 Manipulate and simplify algebraic, exponential, logarithmic, and trigonometric expressions.
 Critical Thinking: Students will be able to demonstrate higherorder thinking skills about issues, problems, and explanations for which multiple solutions are possible. Students will be able to explore problems and, where possible, solve them. Students will be able to develop, test, and evaluate rival hypotheses. Students will be able to construct sound arguments and evaluate the arguments of others.
 Solve application problems that involve algebraic, exponential, logarithmic, and trigonometric functions.
 Critical Thinking: Students will be able to demonstrate higherorder thinking skills about issues, problems, and explanations for which multiple solutions are possible. Students will be able to explore problems and, where possible, solve them. Students will be able to develop, test, and evaluate rival hypotheses. Students will be able to construct sound arguments and evaluate the arguments of others.
 Prove trigonometric identities.
 Critical Thinking: Students will be able to demonstrate higherorder thinking skills about issues, problems, and explanations for which multiple solutions are possible. Students will be able to explore problems and, where possible, solve them. Students will be able to develop, test, and evaluate rival hypotheses. Students will be able to construct sound arguments and evaluate the arguments of others.
Course Content:
 Coordinate Systems
 Rectangular
 Polar
 Equations
 Types of equations
 Rational
 Linear
 Radical
 Polynomial
 Exponential
 Trigonometric
 Logarithmic
 Absolute value
 Polar
 Parametric
 Systems of equations
 Solve
 Intercepts
 Types of equations
 Functions
 Definition
 Properties
 Domain
 Range
 Period
 Amplitude
 Phase Shift
 Evaluation
 Types of Functions
 Linear
 Polynomial
 Rational
 Radical
 Exponential
 Absolute Value
 Logarithmic
 Trigonometric and Their Inverses
 Graphs
 Asymptotic Behavior
 Intercepts
 Vertices
 Symmetry
 Operations on Functions
 Algebra of Functions
 Transformations
 Reflections
 Compositions
 Inverses
 Real Zeros
 Complex Zeros
 Inequalities
 Linear
 Nonlinear
 Absolute Value
 Systems of Inequalities
 Geometry
 Distance Formula
 Pythagorean Theorem
 Euclid's Five Postulates
 Parallel Postulate and Corollaries
 Area
 Volume
 Triangles
 Special Right Triangles
 Other Types of Triangles
 Similarity
 Relationships Between Angles and Sides
 Intersecting Lines
 Circle
 Arcs
 Chords
 Degrees
 Radians
 Unit Circle
 Trigonometry
 Definitions of Trigonometric Functions
 Right Angle Definition
 Unit Circle Definition
 Rectangular Coordinate System Definition
 Simplifying trigonometric identities and formulas
 Inverse trigonometric identities and formulas
 Proving Identities
 Law of Sines
 Law of Cosines
 Applications of Right and Oblique Triangles
 Definitions of Trigonometric Functions
 DeMoivre's Theorem and Applications
 Conic Sections
 Sequences and Series
 Binomial Theorem.
 Mathematical Induction
 Introduction to Vectors
 Magnitude and Direction
 Addition
 Scalar Multiplication
 Component Form
 Vector component Form
Methods of Instruction:
Methods of instruction used to achieve student learning outcomes may include, but are not limited to, the following activities:
 Lectures, discussions, and demonstrations on graphing polynomials and rational functions, applying functions to model real world applications, and manipulating and simplifying trigonometric expressions.
 Calculators or computers may be used for selected topics.
 Create small group activities in order to provide an opportunity for students to the practice of verifying trigonometric identities, solving trigonometric equations, triangles, and applications, and recognizing the relationship between functions and their inverses graphically, algebraically, and aided with technology.
 Develop and assign class exercises that build the students abilities to solve systems of equations and inequalities, and graph functions and relations in rectangular coordinates and polar coordinates.
 Design class handouts on the unit circle and basic trigonometric graphs, and applying transformation to the graphs of functions and relations for both visual and verbal learning styles.
 Create flipped classes that transfer instruction and lecture activities accomplished by the student before the class meeting.
 Classroom activities focus on collaborative techniques and facilitation by the instructor.
 Show videos, films, and computer programs that demonstrate the properties of logarithms, how to graph basic trigonometric functions, and how to synthesize results from the graphs and/or equations of functions and relations.
Methods of Evaluation:
Students will be evaluated for progress in and/or mastery of student learning outcomes using methods of evaluation which may include, but are not limited to, the following activities:
 Written assignments designed to ensure the students abilities to solve rational, radical, and polynomial equations, and graph functions and relations in rectangular coordinates and polar coordinates.
 Written homework assignments and/or computerized homework assignments for correct application of trigonometric principles as well as the correct use of symbols and vocabulary of algebra and trigonometry.
 Quizzes and midterm examinations for conceptual understanding as well as correct technique and application of trigonometric principles in identifying special triangles and their related angle and side measures, evaluating the trigonometric function of an angle in degrees and radian measure, manipulating and simplifying a trigonometric expression, solving trigonometric equations, triangles, and applications, graphing the basic trigonometric functions, applying changes in period, phase and amplitude to generate new graphs and proving trigonometric identities.
 Assessment of classroom discovery activities for content knowledge and conceptual understanding.
 Quizzes and midterm examinations designed to assess the ability to find inverse functions, prove trigonometric identities, and synthesize results from the graphs and/or equations of functions and relations.
 Cumulative Final Examination.
Sample Assignments:
OutsideofClass Reading Assignments
 Read and analyze text, examples, and notes covering topics such as evaluating trigonometric expressions, proving identities, graphing trigonometric functions and solving trigonometric equations.
OutsideofClass Writing Assignments
 Use the symbols of arithmetic, algebra, geometry, and trigonometry to manipulate and simplify trigonometric expressions and solve trigonometric equations, triangles and applications.
Other OutsideofClass Assignments
 Complete problems sets that require students to apply functions to model real world applications.
Course Materials:
All materials used in this course will be periodically reviewed to ensure that they are appropriate for college level instruction. Possible texts include the following:
 Stewart, Redlin, Watson. Precalculus: Mathematics for Calculus. 6th Brooks/Cole, 2012.
 Zill, Dewar. Precalculus with Calculus Previews. 6th Jones and Bartlett Learning, 2015.
Codes/Dates:
CB03 TOP Code:
1701.00  Mathematics, General
CB05 NOR Transfer Status: N/A (not in college inventory) (D)
CB05 RIV Transfer Status: Transfers to Both UC/CSU (A)
CB05 NOR Transfer Status: N/A (not in college inventory) (D)
CB05 RIV Transfer Status: Transfers to Both UC/CSU (A)
Board of Trustees Approval Date:
05/15/2018
COR Rev Date:
05/15/2018