Difference between revisions of "ModelCourses/Trigonometry"
Jump to navigation
Jump to search
| (54 intermediate revisions by 4 users not shown) | |||
| Line 1: | Line 1: | ||
| − | = Model MAA WebWork Course - Trigonometry = |
||
| + | {{UnderConstruction}} |
||
| + | |||
| + | === [https://testcourses.webwork.maa.org/webwork2/Trigonometry/ Try out Trigonometry] === |
||
| + | Log in as guest to see the problems. To check answers you will need to install this set into an active WeBWorK course. |
||
== Subject matter == |
== 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. |
||
| + | * The development of trigonometric formulas starting with angles in degrees. |
||
| + | * Right triangles |
||
| + | * Radians and the unit circle formulation |
||
| + | * Standard applications and formulas |
||
| − | == |
+ | == Problem Syllabus and Problem sets == |
| − | * [[ModelCourses/Trigonometry/AnglesAndTriangles|Angles and Triangles]] |
||
| + | * '''Unit 1''' - Definition of Trigonometric Functions using Degrees |
||
| − | * [[ModelCourses/Trigonometry/TrigFunctionsAngles|Trig functions of Angles in standard position]] |
||
| + | ** Angles and Triangles |
||
| − | * [[ModelCourses/Trigonometry/IdentitiesCalculators|Basic Trig Identities and using Calculators]] |
||
| + | ** Trig functions of Angles in standard position |
||
| − | * [[ModelCourses/Trigonometry/RightTriangles|Trig Functions and Right Triangles]] |
||
| + | ** Basic Trig Identities and using Calculators |
||
| − | * [[ModelCourses/Trigonometry/BasicApplications|Basic Applications of Trig Functions]] |
||
| − | * [[ModelCourses/Trigonometry/RadiansAndReferenceAngles|Radian Measure and Reference Angles]] |
||
| − | * [[ModelCourses/Trigonometry/UnitCircle|Trig Functions and the Unit Circle]] |
||
| − | * [[ModelCourses/Trigonometry/TrigGraphs|Graphs of Trig Functions]] |
||
| − | * [[ModelCourses/Trigonometry/MoreApplications|More Application of Trig Functions]] |
||
| − | * [[ModelCourses/Trigonometry/SumDifferenceFormulas|Sum and Difference Identities]] |
||
| − | * [[ModelCourses/Trigonometry/ProductAndMoreFormulas|Product and other Identities]] |
||
| − | * [[ModelCourses/Trigonometry/InverseTrigFunctions|Inverse Trig functions]] |
||
| − | * [[ModelCourses/Trigonometry/LawOfSines|Law of Sines with Applications]] |
||
| − | * [[ModelCourses/Trigonometry/LawOfCosines|Law of Cosines with Applications]] |
||
| − | * [[ModelCourses/Trigonometry/ComplexNumbers|Complex numbers and Trigonometry]] |
||
| − | * [[ModelCourses/Trigonometry/PolarCoordinates|Polar Coordinates]] |
||
| − | * [[ModelCourses/Trigonometry/ParametricEquations|Parametric Equations]] |
||
| − | * [[ModelCourses/Trigonometry/ConicSections|Conic Sections]] |
||
| − | == Problem sets == |
||
| + | * '''Unit 2''' - Right Triangle Trigonometry |
||
| − | These will be added later. Right now, the links are just to the respective problem syllabus. |
||
| + | ** Trig Functions and Right Triangles |
||
| − | * [[ModelCourses/Trigonometry/AnglesAndTriangles|Angles and Triangles]] |
||
| + | ** Basic Applications of Trig Functions |
||
| − | * [[ModelCourses/Trigonometry/TrigFunctionsAngles|Trig functions of Angles in standard position]] |
||
| + | |||
| − | * [[ModelCourses/Trigonometry/IdentitiesCalculators|Basic Trig Identities and using Calculators]] |
||
| + | * '''Unit 3''' - Radian measure and Trigonometric Functions on the Unit Circle |
||
| − | * [[ModelCourses/Trigonometry/RightTriangles|Trig Functions and Right Triangles]] |
||
| + | ** Radian Measure and Reference Angles |
||
| − | * [[ModelCourses/Trigonometry/BasicApplications|Basic Applications of Trig Functions]] |
||
| + | ** Trig Functions and the Unit Circle |
||
| − | * [[ModelCourses/Trigonometry/RadiansAndReferenceAngles|Radian Measure and Reference Angles]] |
||
| + | |||
| − | * [[ModelCourses/Trigonometry/UnitCircle|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 |
||
| + | |||
| + | [[ Course broken down into downloadable parts | Expanded version and course download ]] |
||
== Readings == |
== Readings == |
||
| Line 52: | Line 44: | ||
* |
* |
||
| − | == Problem Set Review == |
||
| + | [[Category:Model Courses]] |
||
| − | * Initially created by John Travis |
||
| − | * Reviewed and edited by ... |
||
| − | |||
| − | |||
| − | [[ModelCourses]] |
||
Latest revision as of 13:50, 4 June 2014
|
This article is under construction. Use the information herein with caution until this message is removed. |
Try out Trigonometry
Log in as guest to see the problems. To check answers you will need to install this set into an active WeBWorK course.
Subject matter
- The development of trigonometric formulas starting with angles in degrees.
- Right triangles
- Radians and the unit circle formulation
- Standard applications and formulas
Problem Syllabus and Problem sets
- Unit 1 - Definition of Trigonometric Functions using Degrees
- Angles and Triangles
- Trig functions of Angles in standard position
- Basic Trig Identities and using Calculators
- 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
Expanded version and course download
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.
