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Tych Brahe Planetarium in Copenhagen

Precalculus - Unit Six

The Math of Music


In this unit you will explore more deeply how trigonometry applies to music theory. In order to promote a book, you will build a homemade musical instrument and tune the instrument using trigonometric graphs. You will create a presentation to persuade publishing companies to publish your book. The presentation will include excerpts from your book relating the instrument you build to its mathematical connections.

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

  • Lessons
  • Other Resources


Lessons

  • Lesson 1: Trigonometry Basics
    • 6.1 Investigation - The Unit Circle
    • 6.1 Practice - Trigonometry Basics - Practice

  • Lesson 2: Math and Music
    • 6.2 Investigation - Spaghetti Graph
    • 6.2 Practice - Math and Music: Vocabulary Research

  • Lesson 3: Graphs of Sine and Cosine
    • 6.3 Investigation - Seeing Music
    • 6.3 Practice - Graphs of Sine and Cosine - Practice

  • Lesson 4: Turning Music Into Math
    • 6.4 Investigation - Turning Music Into Math
    • 6.4 Practice - More Trig Graphs - Practice

  • Lesson 5: Digging Deeper into the Math of Music
    • 6.5 Investigation - Overtones
    • 6.5 Practice - Triangle Trig Review

  • Lesson 6: The Laws Of Sines And Cosines
    • 6.6 Investigation - Digging Deeper into Triangle Trig
    • 6.6 Practice - The Laws Of Sines And Cosines - Practice

  • Lesson 7: Tangent Lines and Tangent Functions
    • 6.7 Investigation - Off on a Tangent
    • 6.7 Practice - Tangent Lines and Tangent Functions - Practice

  • Lesson 8: Inverse Trigonometric Functions
    • 6.8 Investigation - Can I Get an Inverse?
    • 6.8 Practice - Inverse Trigonometric Functions - Practice

  • Lesson 9: Trigonometric Identities
    • 6.9 Lesson - Trigonometric Identities/li>







Resources - Analytic Trigonometry

The following are links to resources for Analytic Trigonometry:

  • Entire Unit - Coming Soon

  • Analytic Trigonometry - Entire unit on Khan Academy



The following are other free resources:

  • GeoGebra - Free online math tools

  • Desmos - Free online graphing calculator







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