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5-Minute Check Lesson 7-1A

5-Minute Check Lesson 7-1A. Chapter 7. Trigonometric Identities and Equations. Section 7.1. Basic Trigonometric Identities. Definitions Identity – A statement of equality between two expressions that is true for all values of the variable(s) for which the expressions are defined. ex:

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5-Minute Check Lesson 7-1A

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  1. 5-Minute Check Lesson 7-1A

  2. Chapter 7 Trigonometric Identities and Equations

  3. Section 7.1 Basic Trigonometric Identities

  4. Definitions Identity – A statement of equality between two expressions that is true for all values of the variable(s) for which the expressions are defined. ex: Trigonometric Identity – is an identity involving trigonometric expressions. ex: Reciprocal functions – (We talked about this previously… this is just review) Opposite Angle Identities

  5. Definitions continued Quotient Identities – Pythagorean Identities – Recall with the unit circle we knew : And we know : By substitution : Which we write as: If we divide both sides by sine… If we divide both sides by cosine…

  6. Examples Use the given information to find the trigonometric values If , find . If find when If , find when Prove that each equation is not a trigonometric identify by producing a counterexample

  7. More Examples: Simplify: Look for any GCFs: * ) Look for any identities: * Change everything to sines and cosines Simplify Simplify Simplify: Simplify: THESE STEPS ARE NOT IN ANY ORDER. EACH PROBLEM IS SPECIAL AND YOU MUST OPEN YOUR MIND TO HOW TO SOLVE THEM. Your answers will always be 1 term, 1 number or a binomial left with sine and cosine only 

  8. Homework: Page 427: #19 – 51 Odd, 57, 69

  9. You Try It

  10. You try It

  11. Section 7.2 Verify Trigonometric Identities

  12. Suggestions for Verifying trigonometric Identities Transform the more complicated side of the equation into the simplier side. Substitute one or more basic trigonometric identity to simplify expression. Factor or multiply to simplify Multiply expressions by an expression equal to 1. Express all trigonometric functions in terms of sine and cosine. Example: Verify that

  13. Lesson Overview 7-2A

  14. Lesson Overview 7-2B

  15. Lesson Overview 7-2C

  16. You Try It

  17. You Try It

  18. Section 7.3 Sum and Difference Identities

  19. Sum and Difference Identities Sum/Difference Identity for Sine *SINE = SIGN SAME* Sum/Difference Identity for Cosine *COSINE = NO SIGN SAME* Sum/Difference Identity of Tangent *TANGENT – SAME/DIFFERENT*

  20. Lesson Overview 7-3A

  21. Lesson Overview 7-3B

  22. Lesson Overview 7-3C

  23. Examples Find the exact value if and

  24. Homework: Page 442: #15-31 Odd, 34-38 All, 40,42

  25. 5-Minute Check Lesson 7-4A

  26. 5-Minute Check Lesson 7-4B

  27. Lesson Overview 7-4A

  28. Lesson Overview 7-4B

  29. 5-Minute Check Lesson 7-5A

  30. 5-Minute Check Lesson 7-5B

  31. Lesson Overview 7-5A

  32. 5-Minute Check Lesson 7-6A

  33. Lesson Overview 7-6A

  34. Lesson Overview 7-6B

  35. 5-Minute Check Lesson 7-7A

  36. 5-Minute Check Lesson 7-7B

  37. Lesson Overview 7-7A

  38. Lesson Overview 7-7B

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