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Summer Solstice in Antarctica

Unit 1 - Trigonometry

In this unit, you will explore how the trigonometric ratios from high school Geometry relate to circles. First, you will explore the height of a rider on a Ferris Wheel and develop precise definitions of sine and cosine (as well as tangent and the co-functions) using transformational geometry. This precision will lead to a discussion of a mathematically natural unit of rotational measure, called the radian. You will also explore the graphs of periodic functions, and use them to model new situations and discover important properties of trigonometric functions. Pictured above is a time-lapse photo of the Antarctica Observatory over a course of 24-hours showing the sun as it "appears" to move across the sky. Have you seen this type of curve before?

Click on a link to jump ahead to the following sections:

  • Lessons
  • Other Resources


Trigonometry

Lessons

  • Lesson 1: Revolutionary Thinking
    • 1.1 Investigation - George W. Ferris’ Day Off
    • 1.1 Practice - Networks - Practice
    • Blank - Blank Ferris Wheel/li>

  • Lesson 2: Trig Basics
    • 1.2 Investigation - Do You Know “Sine” Language?
    • 1.2 Practice - Sine Language - Practice

  • Lesson 3: The Unit Circle
    • 1.3 Investigation - More "Sine" Language
    • 1.3 Practice - Unit Circle - Practice

  • Lesson 4: Graphing Periodic Functions
    • 1.4 Investigation - More Ferris Wheels
    • 1.4 Practice - Graphing Periodic Functions - Practice

  • Lesson 5: The Cosine as a Functions of Angular Rotations
    • 1.5 Investigation - Moving Shadows
    • 1.5 Practice - Cosine - Practice

  • Lesson 6: Discovering Radians
    • 1.6 Investigation - Diggin’ It
    • 1.6 Practice - Radians - Practice

  • Lesson 7: Thinking in Radians
    • 1.7 Investigation - Staking It
    • 1.7 Practice - Thinking in Radians - Practice

  • Lesson 8: Radians and Arc Length
    • 1.8 Investigation - “Sine”ing and “Cosine”ing It
    • 1.8 Practice - Radians and Arc Length - Practice

  • Lesson 9: Mastering Radian Measures
    • 1.9 Investigation - Water Wheels and the Unit Circle/li>
    • 1.9 Practice - Water Wheels - Practice

  • Lesson 10: Transformations of Trig Functions
    • 1.10 Investigation - High Noon and Sunset Shadows
    • 1.10 Practice - Transformations - Practice

  • Lesson 11: Modeling With Trig
    • 1.11 Investigation - HighTide
    • 1.11 Practice - Modeling With Trig - Practice

  • Lesson 12: More Modeling With Trig
    • 1.12 Investigation - Getting on the Right Wavelength
    • 1.12 Practice - Right Wavelength - Practice

  • Lesson 13: Extending Definitions
    • 1.13 Investigation - Off on a Tangent
    • 1.13 Practice - Tangent - Practice

  • Lesson 14: Trig Identities
    • 1.14 Investigation -1.14 Maintaining Your Identity
    • 1.14 Practice - Trig Identities - Practice

  • Lesson 15: Circular Grids
    • 1.15 Investigation - The Amazing Inverse Race
    • 1.15 Practice - Inverse - Practice







Resources - Trigonometry

The following are links to resources for Trigonometry:

  • Entire Unit - Coming Soon




The following are other free resources:

  • GeoGebra - Free online math tools

  • Desmos - Free online graphing calculator






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