ModelCourses/Trigonometry

Model MAA WebWork Course - Trigonometry

Subject matter

• Trigonometry is the study of triangles and relationships between the measurements of the lengths of triangle sides. This model course covers the development of trigonometric formulas starting with angles in degrees. Proceeds to triangles and then to radians and the unit circle formulation. Standard applications and formulas.

A Problem Syllabus

• Angles and Triangles
• Trig functions of Angles in standard position
• Basic Trig Identities and using Calculators
• Trig Functions and Right Triangles
• Basic Applications of Trig Functions
• Radian Measure and Reference Angles
• Trig Functions and the Unit Circle
• Graphs of Trig Functions
• More Application of Trig Functions
• Inverse Trig functions
• Sum and Difference Identities
• Product and other Identities
• Trig Equations involving One Angle
• Trig Equations involving Multiple Angles
• Law of Sines with Applications
• Law of Cosines with Applications
• Complex numbers and Trigonometry
• Polar Coordinates
• Parametric Equations
• Conic Sections

Problem sets

These will be added later. Right now, the links are just to the respective problem syllabus. Eventually these will link to zipped problem and header material.

If we go with Dick's suggestion we would want two links for each unit or subsection, one of which would be for the reading problems and one for the regular problems.

Entire Course

• Unit 1 - Definition of Trigonometric Functions using Degrees
  • Angles and Triangles
  • Trig functions of Angles in standard position
  • Basic Trig Identities and using Calculators

[Access]

• Unit 2 - Right Triangle Trigonometry
  • Trig Functions and Right Triangles
  • Basic Applications of Trig Functions
• Unit 3 - Radian measure and Trigonometric Functions on the Unit Circle
  • Radian Measure and Reference Angles
  • Trig Functions and the Unit Circle
• Unit 4 - Graphs of Trig Functions
  • Graphs of Trig Functions
  • More Application of Trig Functions
  • Inverse Trig functions
• Unit 5 - Identities and Trig Formulas
  • Sum and Difference Identities
  • Product and other Identities
• Unit 6 - Trigonometric Equations
  • Equations involving a Single Angle
  • Equations involving Multiple Angles
• Unit 7 - General Triangle Trigonometry
  • Law of Sines with Applications
  • Law of Cosines with Applications
• Unit 8 - Trigonometry with Complex Numbers and Polar Coordinates
  • Complex numbers and Trigonometry
  • Polar Coordinates
  • Parametric Equations
  • Conic Sections

Readings

A few selected reading/research projects are included as special homework problems in the model course homework sets. Each of these projects are completely defined and include a few numerical questions to encourage the students to start their information search. Correctly answering these numerical questions give complete credit for the "homework" problems but the paper submitted later would be expected to be somewhat more extensive. It is not expected that the papers will be exhaustive but more like a web search and compilation with perhaps some examples. If an instructor does not want to pursue written work, these problems can be deleted without detracting from the problem syllabus.

• Historical look into the development of the Pythagorean Theorem and focus on real-life applications.
• Investigation into nautical miles and the relationship to angular measure, surface distance and applications.

Review of Trigonometry Model Course

• Initially created by John Travis, Fall 2011 (Draft is available live at "http://math.mc.edu/webwork2/". Click on 102.)
• Reviewed and edited by ...