Discipline: Mathematics
Originator: Marc Sanchez

Riverside Community College District
Integrated Course Outline of Record

Mathematics 36
MAT-36 : Trigonometry
College:
Lecture Hours: 72.000
Outside-of-Class Hours: 144.000
Units: 4.00
Grading Methods: Pass/No Pass
Letter Grade
Course Description
Prerequisite: MAT-35 and MAT-53 or Appropriate placement
Course Credit Recommendation: Degree Credit

The study of trigonometric functions, their inverses and their graphs; identities and proofs related to trigonometric expressions; solving trigonometric equations; solving right triangles; solving oblique triangles using the law of sines and cosines; polar coordinates; complex numbers; introduction to vectors and elements of geometry important to the foundation of trigonometry. 72 hours lecture. (Letter Grade or Pass/No Pass option)
Short Description for Class Schedule
An introduction to the trigonometric functions, their identities, graphs and applications, accompanied by essential topics of geometry.
Entrance Skills:
Before entering the course, students should be able to demonstrate the following skills:
  1. Simplify algebraic expressions using correct mathematical symbols and language.
    • MAT-35 - Simplify algebraic expressions using correct mathematical symbols and language.
  2. Identify and apply appropriate methods to solve rational, radical, exponential, and logarithmic equations.
    • MAT-35 - Identify and apply appropriate methods to solve rational, radical, exponential, and logarithmic equations.
  3. Solve applications that require writing and solving equations. Communicate solution in the context of the problem.
    • MAT-35 - Solve applications that require writing and solving equations. Communicate solution in the context of the problem.
  4. Graph linear and basic nonlinear functions.
    • MAT-35 - Graph linear and basic nonlinear functions.
  5. Solve problems involving angles and transversals.
    • MAT-53 - Solve problems involving angles and transversals.
  6. Solve applications using the Pythagorean Theorem, special right triangles, and the components of regular and non-regular polygons.
    • MAT-53 - Solve applications using the Pythagorean Theorem, special right triangles, and the components of regular and non-regular polygons.
Course Objectives:
Upon successful completion of the course, students should be able to demonstrate the following activities:
  1. Identify special triangles and their related angle and side measurements.
  2. Evaluate the trigonometric function of an angle in degree and radian measure.
  3. Manipulate and simplify a trigonometric expression.
  4. Solve trigonometric equations, triangles, and applications.
  5. Graph the basic trigonometric functions and apply changes in period, phase and amplitude to generate new graphs.
  6. Evaluate and graph inverse trigonometric functions.
  7. Prove trigonometric identities.
  8. Convert between polar and rectangular coordinates and equations.
  9. Graph polar equations.
  10. Convert complex numbers between rectangular and polar form. Multiplication and division in polar form.
  11. Calculate powers and roots of complex numbers using DeMoivre's Theorem.
  12. Represent a vector (a quantity with magnitude and direction) in the form of < a,b > and ai+bj.
Student Learning Outcomes:
Upon successful completion of the course, students should be able to demonstrate the following skills:
  1. Graph 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.
  2. Solve trigonometric equations.
    • 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.
  3. Solve applications involving triangles 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.
    • 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.
  4. 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. Introductory Concepts
    1. Rectangular coordinates
    2. Angles and circular measure
  2. Geometry Review
    1. Arcs, chords, and arc length
    2. Parallel lines and transversals
    3. Conguency statements for triangles
    4. Area of a circle and sector
  3. Triangles
    1. Special right triangles
    2. Similarity
    3. Relationships between angles and sides
  4. Trigonometric Functions
    1. The six trigonometric functions defined using the rectangular coordinate system, right triangles and the unit circle
    2. Trigonometric functions of special angles
  5. Trigonometric Identities  
    1. Pythagorean, reciprocal, ratio, sum and difference, double, half, product to sum and sum to product 
    2. Simplifying trigonometric expressions using identities
    3. Proving trigonometric identities
  6. Graphing Trigonometric Functions
    1. Domain and range
    2. Basic cycles
    3. Period, amplitude, phase shift, vertical shift, reflections and asymptotes
  7. Inverse Trigonometric Functions and their Graphs
    1. Evaluating and simplifying inverse trigonometric expressions
    2. Graphs of inverse trigonometric functions
  8. Trigonometric Equations
    1. Solutions on an interval
    2. All solutions
    3. Equations that require trigonometric identities
    4. Equations involving multiple angles
  9. Solving Triangles and Applications
    1. Solving right triangles
    2. Law of Sines
    3. Law of Cosines
    4. Applications to vectors
  10. Polar Coordinates and Equations
    1. Polar coordinates and rectangular coordinates
    2. Polar equations and rectangular equations
    3. Graphing polar equations
  11. Complex Numbers
    1. Addition, subtraction, multiplication, and division
    2. Trigonometric form
    3. Multiplication and division in trigonometric form
    4. De Moivre's Theorem and roots of a complex number
  12. Introduction to Vectors
    1. Geometric interpretation
    2. Addition, subtraction and scalar multiplication
    3. Component form
    4. Applications
Additional Laboratory Content
Methods of Instruction:
Methods of instruction used to achieve student learning outcomes may include, but are not limited to, the following activities:
  • Class lectures, discussions, and demonstrations of the four basic operations as applied to identifying special triangles and their related angle and side measures, evaluating the trigonometric function of an angle in degree 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. 
  • Drills and pattern practices utilizing hand-outs and/or computer-based tools in order to assist the students in mastering the techniques involved in identifying special triangles and their related angle and side measures, evaluating the trigonometric function of an angle in degree 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. 
  • Provision and employment of a variety of learning resources such as videos, slides, audio tapes, computer-based tools, manipulatives, and worksheets in order to address multiple learning styles and to reinforce material.
  • Pair and small group activities, discussions, and exercises in order to promote mathematics discovery and enhance problem solving skills.
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 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/final 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 degree 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.
Sample Assignments:
Outside-of-Class 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.
Outside-of-Class Writing Assignments
  • Use the symbols of algebra, geometry and trigonometry while solving application problems.
Other Outside-of-Class Assignments
  • Problem sets that require students to perform algebraic operations on trigonometric expressions, solve trigonometric equations, or graph trigonometric functions.
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:
  • Blitzer, Charles F. Trigonometry. 2nd Pearson, 2017.
  • McKeague, Charles P. . Trigonometry. 8th Thomson Brooks/Cole, 2016.
  • (In addition to the textbooks listed, instructors may also choose open source textbooks which often come at little or no cost to the students.)
Codes/Dates:
CB03 TOP Code: 1701.00 - Mathematics, General
CB05 MOV Transfer Status: Transfers to CSU Only (B)
CB05 NOR Transfer Status: Transfers to CSU Only (B)
CB05 RIV Transfer Status: Transfers to CSU Only (B)
C-ID#: MATH 851
Board of Trustees Approval Date: 01/15/2019
COR Rev Date: 01/15/2019