Discipline: Mathematics
Originator: Ernesto Reyes

# Riverside Community College District Integrated Course Outline of Record

Mathematics 23
 MAT-23 : Trigonometry & Precalculus College: RIV Lecture Hours: 90.000 Lab Hours: 54.000 Outside-of-Class Hours: 180.000 Units: 6.00 Grading Methods: Pass/No Pass Letter Grade
Course Description
Prerequisite: MAT-35 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:
1. Apply the basic operations of algebra on the set of real and complex numbers, polynomials, rational and radical expressions
• MAT-35 - Simplify algebraic expressions using correct mathematical symbols and language.
2. Solve linear, rational, quadratic, exponential, radical, logarithmic, and absolute value equations.
• MAT-35 - Identify and apply appropriate methods to solve rational, radical, exponential, and logarithmic equations.
3. Solve inequalities and systems of equations.
• MAT-35 - Simplify algebraic expressions using correct mathematical symbols and language.
• MAT-35 - Simplify algebraic expressions using correct mathematical symbols and language.
4. Graph basic functions.
• MAT-35 - Graph linear and basic nonlinear functions.
5. Apply basic operations on functions.
• MAT-35 - 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:
1. Graph functions, relations, and polar equations in rectangular coordinates and polar coordinates.
2. Synthesize results from the graphs and/or equations of functions and relations.
3. Apply transformations to the graphs of functions and relations.
4. Recognize the relationship between functions and their inverses graphically and algebraically.
5. Solve systems of equations and inequalities.
6. Apply functions to model real world applications.
7. Identify special triangles and their related angle and side measures.
8. Evaluate the trigonometric function of an angle given in degree and radian measure.
9. Manipulate and simplify a trigonometric expression.
10. Solve trigonometric equations, triangles, and applications.
11. Graph the basic trigonometric functions and apply changes in period, phase shift and amplitude to generate new graphs.
12. Prove trigonometric identities.
13. Solve and apply equations including rational, linear, polynomial, exponential, absolute value, radical, and logarithmic.
14. Solve linear, nonlinear and absolute value inequalities.
15. Graph the basic trigonometric functions and apply changes in period, phase shift and amplitude to generate new graphs.
16. Evaluate and graph inverse trigonometric functions.
17. Convert between polar and rectangular coordinates.
18. Calculate powers and roots of complex numbers using DeMoivre's Theorem.
19. Introduction to vectors.
20. Solve applications involving the Pythagorean theorem and special right triangles.
21. Solve applications involving angles and a transversal.
22. Solve applications involving the distance formula.
23. Solve applications involving similar triangles.
24. 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:
1. Solve algebraic, exponential, logarithmic, and trigonometric equations and algebraic inequalities using appropriate techniques.
• Critical Thinking: Students will be able to demonstrate higher-order 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.
2. 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.
3. Manipulate and simplify algebraic, exponential, logarithmic, and trigonometric expressions.
• Critical Thinking: Students will be able to demonstrate higher-order 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.
4. Solve application problems that involve algebraic, exponential, logarithmic, and trigonometric functions.
• Critical Thinking: Students will be able to demonstrate higher-order 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.
5. Prove trigonometric identities.
• Critical Thinking: Students will be able to demonstrate higher-order 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:
1. Coordinate Systems
1. Rectangular
2. Polar
2. Equations
1. Types of equations
1. Rational
2. Linear
4. Polynomial
5. Exponential
6. Trigonometric
7. Logarithmic
8. Absolute value
9. Polar
10. Parametric
2. Systems of equations
3. Solve
4. Intercepts
3. Functions
1. Definition
2. Properties
1. Domain
2. Range
3. Period
4. Amplitude
5. Phase Shift
3. Evaluation
4. Types of Functions
1. Linear
2. Polynomial
3. Rational
5. Exponential
6. Absolute Value
7. Logarithmic
8. Trigonometric and Their Inverses
5. Graphs
1. Asymptotic Behavior
2. Intercepts
3. Vertices
4. Symmetry
6. Operations on Functions
1. Algebra of Functions
2. Transformations
3. Reflections
4. Compositions
5. Inverses
7. Real Zeros
8. Complex Zeros
4. Inequalities
1. Linear
2. Non-linear
3. Absolute Value
4. Systems of Inequalities
5. Geometry
1. Distance Formula
2. Pythagorean Theorem
3. Euclid's Five Postulates
4. Parallel Postulate and Corollaries
5. Area
6. Volume
7. Triangles
1. Special Right Triangles
2. Other Types of Triangles
3. Similarity
4. Relationships Between Angles and Sides
5. Intersecting Lines
8. Circle
1. Arcs
2. Chords
3. Degrees
5. Unit Circle
6. Trigonometry
1. Definitions of Trigonometric Functions
1. Right Angle Definition
2. Unit Circle Definition
3. Rectangular Coordinate System Definition
2. Simplifying trigonometric identities and formulas
3. Inverse trigonometric identities and formulas
4. Proving Identities
5. Law of Sines
6. Law of Cosines
7. Applications of Right and Oblique Triangles
7. DeMoivre's Theorem and Applications
8. Conic Sections
9. Sequences and Series
10. Binomial Theorem.
11. Mathematical Induction
12. Introduction to Vectors
1. Magnitude and Direction
3. Scalar Multiplication
4. Component Form
5. 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:
• Read and analyze text, examples, and notes covering topics such as evaluating trigonometric expressions, proving identities, graphing trigonometric functions and solving trigonometric equations.

Outside-of-Class 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 Outside-of-Class 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)
Board of Trustees Approval Date: 05/15/2018
COR Rev Date: 05/15/2018