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Mastering Sine and Cosine Graphs: Shifts, Amplitude, and Period

Explore graphing sine and cosine functions with various amplitudes, periods, shifts, and cycles for a deep understanding. Learn through illustrative examples and step-by-step explanations.

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Mastering Sine and Cosine Graphs: Shifts, Amplitude, and Period

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  1. Section 4.5Graphs of Sine and Cosine Functions

  2. Continuation of the previous problem showing 3 cycles

  3. Graphing y=2 Sin x

  4. Graphing y=½ Sin x

  5. Graphing y=-2 Sin x

  6. Graphing y=3 Sin 2x

  7. The Effect of Horizontally Shifting the Graph

  8. Example

  9. Example

  10. Example

  11. Example

  12. Example

  13. Example

  14. Cosine with a Different Amplitude and Period

  15. Example

  16. Example

  17. Vertical Shifts of Sinusoidal Graphs

  18. Cosine Function with a Vertical Shift

  19. Example

  20. Example

  21. Example 20 10 2 6 10 14 18 22 26 The number of hours after midnight.

  22. (a) (b) (c) (d)

  23. (a) (b) (c) (d)

  24. (a) (b) (c) (d)

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