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Unlocking Trigonometric Identities for Calculus Success

Learn about Double-Angle, Power-Reducing, and Half-Angle Identities, and how to solve Trigonometric Equations. Prove and apply essential identities in calculus courses.

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Unlocking Trigonometric Identities for Calculus Success

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Presentation Transcript

  1. Warm Up What is the Pythagorean Identity?

  2. Goal: Apply the double-angle identities. 5.4 Multiple Angle Identities

  3. What you’ll learn about • Double-Angle Identities • Power-Reducing Identities • Half-Angle Identities • Solving Trigonometric Equations … and why These identities are useful in calculus courses.

  4. Double Angle Identities

  5. Proving a Double-Angle Identity Prove.

  6. Proving a Double-Angle Identity

  7. When α = 30°, verify the identity for sin 2α.

  8. #1 Rewrite in a simpler form.

  9. #2 Rewrite in a simpler form.

  10. #3 Rewrite in a simpler form.

  11. #4 Rewrite in a simpler form.

  12. #5 Rewrite in a simpler form.

  13. #6 Rewrite in a simpler form.

  14. #7 Evaluate without a calculator.

  15. #8 Evaluate without a calculator.

  16. Half-Angle Identities

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