Discipline: Mathematics Degree Credit  [X]
Non Credit  [ ]
Nondegree Credit  [ ]
Comm Service  [ ]
 

Riverside Community College District
Integrated Course Outline of Record

Mathematics 36


COURSE DESCRIPTION
36 Trigonometry Units: 4.00
 
Prerequisite(s): MAT 35: Intermediate Algebra and MAT 53: College Geometry
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 cosines and the law of sines; elements of geometry important to the foundation of trigonometry. 72 hours lecture.
 
SHORT DESCRIPTION FOR CLASS SCHEDULE
An introduction to the trigonometric functions, their identities and relationships, graphs and applications, accompanied by essential topics of geometry.
 
ADVISORY ENTRY SKILLS
Before entering the course, students will be able to:
  1. Apply the basic operations of algebra on the set of real and complex numbers, polynomials, rational and radical expressions.

  2. Solve linear, rational, quadratic, exponential, radical, logarithmic, and absolute value equations.

  3. Solve inequalities and systems of equations.

  4. Graph basic functions.

  5. Apply basic operations on functions.

  6. Identify types of angles and triangles.

  7. Identify properties of circles and line segments and the angles associated with them.
STUDENT LEARNING OUTCOMES
 Upon successful completion of the course, students should be able to:

Identify special triangles and their related angle and side measures.

  1. Critical Thinking - Generalize appropriately from specific contexts
  2. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  3. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

Evaluate the trigonometric function of an angle in degree and radian measure.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Generalize appropriately from specific contexts
  3. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  4. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

Manipulate and simplify a trigonometric expression.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  3. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

Solve trigonometric equations, triangles, and applications.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Integrate knowledge across a range of contexts
  3. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  4. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

Graph the basic trigonometric functions and apply changes in period, phase and amplitude   to generate new graphs.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Generalize appropriately from specific contexts
  3. Critical Thinking - Integrate knowledge across a range of contexts
  4. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  5. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

Prove trigonometric identities.
   

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Construct sound arguments and evaluate arguments of others
  3. Critical Thinking - Generalize appropriately from specific contexts
  4. Critical Thinking - Integrate knowledge across a range of contexts
  5. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  6. Application of Knowledge - Maintain and transfer academic and technical skills to workplace
 
COURSE CONTENT
  TOPICS
 

1.   Introductory Concepts
      a.   Rectangular coordinates, angles and circular measure.
2.   Triangles
      a.   Special right triangles, types of triangles, similarity,
            relationships of angles and sides, parallel and intersecting
            lines.
3.   Trigonometric Functions
      a.   Definitions of the six trigonometric functions according to both 
            the right triangle, the  unit circle and the rectangular coordinate
            system.
4.   Applications of the right triangle.
5.   Trigonometric Identities  
      a.   Simplifying trigonometric expressions and proving 
            trigonometric identities.
6.   Graphing Trigonometric Functions
      a.   Period, amplitude, phase shift, inverse trigonometric functions.
7.   Trigonometric equations.
8.   Solving Oblique Triangles
      a.   Law of Sines, Law of Cosines
9.   Polar coordinates and equations
10.  DeMoivre’s Theorem and applications
 
METHODS OF INSTRUCTION
 Methods of instruction used to achieve student learning outcomes may include, but are not limited to:

  • 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 learning outcomes by methods of evaluation which may include, but are not limited to:

  • 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.
ASSIGNMENTS

Required Reading Assignments


Required Writing Assignments


Other Outside-of-Class Assignments
 
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:

  • McKeague, Charles P. . Trigonometry. 5th ed. Thomson Brooks/Cole, 2004.
  • Larson, Hostetler, Edwards. Trigonometry a Graphing Approach. 3rd ed. Houghton-Mifflin, 2001.
  • Geometry Supplement book
08/06
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