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Trigonometric Graphs, Identities, and Equations

Trigonometric Graphs, Identities, and Equations. Advanced Algebra Chapter 14. Graphing Sine, Cosine, and Tangent Fucntions—14.1. The functions of sine an cosine shard the following:. The domain of each function is all real numbers The range of each function is Each function is periodic

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Trigonometric Graphs, Identities, and Equations

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  1. Trigonometric Graphs, Identities, and Equations Advanced AlgebraChapter 14

  2. Graphing Sine, Cosine, and Tangent Fucntions—14.1

  3. The functions of sine an cosine shard the following: • The domain of each function is all real numbers • The range of each function is • Each function is periodic • Each graph has a repeating portion called a cycle • 1 period of a graph is 1 full cycle • Amplitude is the defined as the height of the graph from it’s center • ½ it’s total height • Amplitude is always positive

  4. Sine • Period: • Amp:

  5. Cosine • Period: • Amp:

  6. Graphing Functions • For the trig functions and • If a is positive: Graph opens “normal” • If a is negative: Graph opens “opposite”

  7. Graphing Functions

  8. Graphing Functions

  9. Graphing Functions

  10. Graphing Functions

  11. Graphing Functions

  12. p.835#17-28, 32-35

  13. Translations and Reflections of Trigonometric Graphs—14.2

  14. Translations • To obtain the graph of ortransform the graph of oras follows: • Vertical shift • Shift the graph k units vertically • Horizontal shift • Shift the graph h units horizontally • Reflection • If a is less than zero, flip graph over x-axis

  15. Graphing Functions

  16. Graphing Functions

  17. Graphing Functions

  18. Graphing Functions

  19. Graphing Functions

  20. Graphing Functions

  21. p.844#17-22, 26-31, 32-35

  22. Verifying Trig Identities—14.3

  23. Verify that…

  24. Verify that…

  25. Verify that…

  26. Verify that…

  27. Verify that…

  28. Verify that…

  29. p.852#16,17,20,21,22,28-47 • 10 point

  30. Solving Trig Equations—14.4

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