The Trigonometry: A Unit Circle Approach that Prepares for Calculus Content Pack is a trigonometry course presented using the unit circle approach that you can use as a customizable starting point to a complete college course in Möbius. This unit circle approach fits much better with the concept of functions. In addition, this approach allows most topics in trigonometry to be built upon the unit circle. This customizable resource contains 5 units of sectioned lessons and assignments enhanced with Möbius capabilities including algorithmic questions, embedded videos, and end-of-lesson quizzes.

How does Möbius take this Content Pack to the next level?

Course Structure

  • All content is organized into 5 units for easy navigation
  • Course materials provide a solid foundation for creating your course offering which include 27 lessons with illustrative visualizations and video elements
  • Different forms of assessment materials are distributed across 27 assignments to evaluate student comprehension through a variety of different question types
  • Pull from a vast selection of over 830 questions that you can use to create your own lessons and assignments or supplement existing ones
5 units
27 lessons
27 assignments
830+ questions

Unit 1: Introduction to the Language of Mathematics

  • 1.1 Angles and Their Measure

  • 1.2 Applications

  • 1.3 The Unit Circle and the Trigonometric Functions

  • 1.4 Fundamental Identities

  • 1.5 Trigonometric Function Values of Any Angle, Further Identities, and Properties

Unit 2: Graphs, Applications, and Inverse Trigonometric Functions

  • 2.1 Graphs of Sine and Cosine Functions

  • 2.2 Modeling Periodic Behavior and Applications

  • 2.3 Graphs of Tangent, Cotangent, Secant, and Cosecant Functions

  • 2.4 Inverse Trigonometric Functions (Part I)

  • 2.5 Inverse Trigonometric Functions (Part II)

Unit 3: Identities and Equations

  • 3.1 Verifying Trigonometric Identities

  • 3.2 Sum and Difference Identities

  • 3.3 Solving Trigonometric Equations (Part I)

  • 3.4 Double Angle, Power-Reducing, and Half-Angle Identities

  • 3.5 Solving Trigonometric Equations (Part II)

  • 3.6 Product-to-Sum and Sum-to-Product Identities

Unit 4: Triangles and Applications

  • 4.1 Alternative Definition of the Trigonometric Functions and Right Triangle Trigonometry

  • 4.2 Right Triangle Trigonometry and Applications

  • 4.3 Law of Sines

  • 4.3 Digital Exercises

  • 4.4 Law of Cosines

  • 4.5 Additional Applications with Triangles

Unit 5: Polar Equations, Complex Numbers, and Vectors

  • 5.1 Polar Coordinates

  • 5.2 Polar Equations and Graphs

  • 5.3 Trigonometric (Polar) Form of Complex Numbers and DeMoivre’s Theorem

  • 5.4 Parametric Equations and Graphs

  • 5.5 Basics of Vectors in the Plane

  • 5.6 Vectors, Dot Product, and Applications

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