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Course Proposals (Drafts)

Course Outlines

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Math 25 --- College Trigonometry

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Catalog Description

A study of trigonometric functions, radian measure, solution of right triangles, graphs of the trigonometric functions, inverse trigonometric functions, trigonometric identities and equations, laws of sines and cosines, solution of oblique triangles, polar coordinates, complex numbers in trigonometric form, De Moivre’s theorem, and conic sections.

Special notes or advisories: A graphing calculator is required.

Prerequisites

Math 120 (or equivalent) with a grade of "C" or better or appropriate score on the math placement exam.

Describe representative skills without which the student would be highly unlikely to succeed: Ability to solve linear, quadratic, absolute value, polynomial, rational, radical, exponential and logarithmic equations analytically, graphically, numerically and verbally in real-world settings. Ability to use technology in the study of these functions.

Recommended Preparation

Course Learning Outcomes

What should the student be able to do as a result of taking this course? State some of the objectives in terms of specific, measurable student accomplishments.

1. Read, write, and speak accurately about mathematical ideas and use correct mathematical notation.
2. Use graphing technology to visualize trigonometric curves, explore mathematical concepts, and verify their work.
3. Use the theories of trigonometric functions and conic sections as fundamental problem-solving tools.
4. Demonstrate the characteristics of an effective learner, such as note-taking, critical reading, communication through writing, verbal discussions, etc.
5. Apply the mathematics of trigonometric functions to real-world problems and applications.
6. Use numerical, graphical, symbolic, and verbal representations to solve problems and communicate with others.

Course Content

• Themes: What themes, if any, are threaded throughout the learning experiences in this course?
  • Functions
  • Critical thinking
  • Problem solving
  • Writing
  • Technology
  • Communication
• 
  
• Concepts: What concepts do students need to understand to demonstrate course outcomes?
  • A multiple-step problem-solving process.
  • The presentation of mathematical solutions in a logical, coherent structure, including the use of writing skills, grammar, and punctuation.
  • The use of the graphing calculator as a fundamental problem-solving tool.
  • The connection between graphs and properties of trigonometric functions.
  • The application of trigonometric functions and conic sections to real-world problems.
  • Properties of trigonometric functions, including definitions, domain, range, their graphs, and the application of these properties to the problem-solving process.
  • The recognition that proper use of algebraic skills is an important tool in multiple problem-solving situations.
• 
  
• Issues: What primary issues or problems, if any, must students understand to achieve course outcomes.
  • The appropriate use of technology in the problem-solving process.
  • The connection between mathematics and the real world.
  • The role of the student in becoming a successful learner.
  • The recognition that the problem-solving skills learned in this class are applicable in future mathematics classes, classes in related fields (such as physics, engineering, etc.) as well as in the real world.
  • The importance of writing mathematics using correct notation and grammar.
  • The limitations of technology.
  • The necessity to read unfamiliar mathematics using their text and other resources.
  • The relationship between degree and radian measure of angles.
  • The importance of radian measure in developing useful formulas.
  • The difference between an identity and a conditional equation.
  • The difference between an exact value and an approximate value.
• 
  
• Skills: What skills must students master to demonstrate course outcomes?
  1. Use a calculator to: find function values and angle measures for the six trigonometric functions; graph a trigonometric function, find an appropriate viewing window, find intersections, zeros, extrema, increasing/decreasing intervals, and inverses; find appropriate mathematical models; approximate solutions to equations and inequalities.
  2. Trigonometric Functions:
  3. • Explain the definitions of trigonometric functions in relation to right triangles.
     • Explain the definitions of trigonometric functions as circular functions in relation to the unit circle.
  4. Linear and Angular Velocity:
  5. • Solve problems involving linear and angular velocity using correct unit conversions.
  6. Graphing Trigonometric Functions:
  7. • Be able to identify the transformations and properties of trigonometric functions including domain, range, symmetry, period, amplitude, phase shift, vertical shift, maximum and minimum values and intercepts and understand their importance in problem solving. Students should be able to find these with and without calculators.
  8. Inverse Functions:
  9. • Identify one-to-one functions analytically.
     • Identify one-to-one functions using the horizontal line test.
     • Compare the graphs of a function and its inverse.
     • Find the inverse of a function.
     • Identify the domain and range intervals of the various inverse trigonometric functions.
     • Apply inverse trigonometric functions to real-world problems.
     • Approximate values of the inverse trigonometric functions using the graphing calculator along with the range intervals.
  10. Identities:
  11. • Determine if an equation is an identity.
      • Verify identities.
  12. Trigonometric Equations:
  13. • Solve trigonometric equations by using trigonometric identities and techniques from algebra.
      • Solve trigonometric equations symbolically, and approximate solutions with graphing calculators.
  14. Oblique Triangles:
  15. • Use the Law of Sines and the Law of Cosines to solve oblique triangles.
      • Solve triangles that involve the ambiguous SSA case of the Law of Sines.
      • Solve applications that require oblique triangles.
  16. Polar Coordinates:
  17. • Convert the coordinates of a point between rectangular and polar form.
      • Convert equations between rectangular and polar form.
      • Graph curves given in polar form.
  18. Complex Numbers:
  19. • Write complex numbers in polar form.
      • Perform algebraic operations on complex numbers, using polar form when appropriate.
      • Use De Moivre's Theorem to compute powers of complex numbers.
      • Find roots of complex numbers in standard form and polar form.
  20. Conic Sections:
  21. • Identify the conic sections by manipulating their equations and writing them in standard form.
      • Graph the conic sections, labeling the center, foci, vertices, directrix, asymptotes, and axes.
      • Solve applications that make use of conic sections.

Representative Learning Activities

What will the students be doing (i.e., Listening to lectures, participating in discussions and/or group activities, attending a field trip, etc.)? Relate the activities directly to the Course Learning Outcomes.

• Listening to lectures
• Participating in group activities and/or assignments
• Participating in class assignments and/or discussions
• Completing homework assignments
• Completing online activities
• Using the graphing calculator and/or mathematical software to complete activities designed to foster a deeper level of understanding of the concepts and skills developed in this class

Assessment Tasks

How will the student show evidence of achieving the Course Learning Outcomes? Indicate which assessments (if any) are required for all sections.

• Representative assessment tasks:
• • In-class examinations and/or quizzes
  • Homework assignments
  • In-class activities
  • Take-home examinations and/or quizzes allow the instructor to include questions and/or exercises that require more in-depth analysis. Extra time allows the students to develop their writing and presentation skills
  • Writing assignments designed to develop communication of mathematical concepts
  • Group and/or individual projects and presentations
  • Portfolios
• Required assessments for all sections – to include but not limited to:
• • Homework assignments
  • At least two proctored, closed-book examinations

Examples of Appropriate Texts or Other Readings

• Author: Hornsby, Lial, Rockwood; Title: A Graphical Approach to College Algebra, Third Edition; Date 2003
• Author: Sullivan; Title: Algebra and Trigonometry, Eighth Edition; Date 2007