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Chapter 5.1

Chapter 5.1. 5.1 Using Fundamental Identities. In this chapter, you will learn how to use the fundamental identities to do the following: Evaluate trigonometric functions Simplify trigonometric expressions Develop additional trigonometric identities Solve trigonometric equations.

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Chapter 5.1

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  1. Chapter 5.1

  2. 5.1 Using Fundamental Identities • In this chapter, you will learn how to use the fundamental identities to do the following: • Evaluate trigonometric functions • Simplify trigonometric expressions • Develop additional trigonometric identities • Solve trigonometric equations

  3. 5.1 Using Fundamental Identities • Using Identities to evaluate a function • Why should you learn this? • In calculus you will use trigonometric identities to simplify an expression. • Ex: Homework p.347 #97 is an example

  4. 5.1 Using Fundamental Identities Quadrant II Quadrant I Quadrant III Quadrant IV

  5. 5.1 Using Fundamental Identities Using Identities to Evaluate a Function Given: Find: The value of all six trigonometric functions *Remember: Once you know the value of Sine and Cosine you can find the values of all six trigonometric functions

  6. 5.1 Using Fundamental Identities Given: *Use the information given to decide which quadrant Which quadrant are we in?1______ Find: The value of all six trigonometric functions Looking at page 340 in your book: Can you see which identity we should use to find the value of sine?

  7. 5.1 Using Fundamental Identities Pythagorean Identity2

  8. 5.1 Using Fundamental Identities Now we know3 :

  9. 5.1 Using Fundamental Identities Now try #11 pg.3454

  10. 5.1 Using Fundamental Identities Simplifying a Trigonometric Expression5 Factor out a Use the distributive property Use the Pythagorean Identity Multiply

  11. 5.1 Using Fundamental Identities Verifying a Trigonometric Identity7

  12. 5.1 Using Fundamental Identities Now try #45 pg.3468 To check graphically, use radian mode graph one side of the equation as and the other side of the equation as . (Select line style for and path style for . )

  13. 5.1 Using Fundamental Identities Factoring Trigonometric Expressions9 a.) b.)

  14. 5.1 Using Fundamental Identities Now try #51 pg.34610

  15. 5.1 Using Fundamental Identities *NOTE: On occasion, factoring or simplifying can best be done by rewriting the expression in terms of just one trigonometric function or in terms of sine or cosine alone. Simplify11:

  16. 5.1 Using Fundamental Identities Now try #67 pg.34612

  17. 5.1 Using Fundamental Identities Enriched Pre-Calculus Rewriting a Trigonometric Equation Rewrite13 so that it is not in fractional form.

  18. 5.1 Using Fundamental Identities Now try #69 pg.34614

  19. 5.1 Using Fundamental Identities Enriched Pre-Calculus Trigonometric Substitutions15 Use the substitution to write as a trigonometric function of .

  20. 5.1 Using Fundamental Identities Now try #81 pg.34716

  21. THE END

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