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Understanding Trigonometric Sum and Difference Identities

Learn about cosine, sine, and tangent of a difference or sum, verifying sinusoids algebraically, and exploring the different algebraic properties of functions. Gain insight into the need for different versions of the same identity.

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Understanding Trigonometric Sum and Difference Identities

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  1. 5.3 Demana, Waits, Foley, Kennedy Sum and Difference Identities

  2. What you’ll learn about • Cosine of a Difference • Cosine of a Sum • Sine of a Difference or Sum • Tangent of a Difference or Sum • Verifying a Sinusoid Algebraically … and why These identities provide clear examples of how different the algebra of functions can be from the algebra of real numbers.

  3. Does the Distributive Law Apply?

  4. Cosine of a Sum or Difference

  5. Example: Using the Cosine-of-a-Difference Identity

  6. Solution

  7. Sine of a Sum or Difference

  8. Example: Using the Sum and Difference Formulas

  9. Solution

  10. Prove the Cofunction Identities

  11. Tangent of a Difference of Sum Why would we need two different versions for the same thing ?

  12. Show that

  13. Example: Expressing a Sum of Sinusoids as a Sinusoid

  14. Solution

  15. Solution

  16. Solution

  17. Solution

  18. Solution

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