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8.2 Sine and Cosine Curves

8.2 Sine and Cosine Curves. Period and Amplitude Changes. Periodic function keeps repeating the same pattern over and over The smallest period of a periodic function is called the fundamental period Amplitude. SINE FUNCTION. Period =2 π. Amplitude = 1. COSINE FUNCTION. Period =2 π.

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8.2 Sine and Cosine Curves

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  1. 8.2 Sine and Cosine Curves Period and Amplitude Changes

  2. Periodic function keeps repeating the same pattern over and over The smallest period of a periodic function is called the fundamental period Amplitude

  3. SINE FUNCTION Period =2π Amplitude = 1

  4. COSINE FUNCTION Period =2π Amplitude = 1

  5. General Form We are going to graph sine and cosine waves with changes to both the amplitude (a) and the period (b). So, the equations will be in the form: or

  6. General Form Where: Amplitude=│a│ Period=2π/b or b=2π/p

  7. To do these, think carefully about: • where to start the wave • how high and low the maximum and minimum values (y-coordinates) should be • how long (x-interval) it should take to complete one full wave

  8. Examples • Graph Amplitude = 3 Period = π

  9. Examples

  10. Examples

  11. Examples • Graph Amplitude = 4 Period =4π

  12. Examples

  13. Examples

  14. Examples

  15. Examples

  16. Examples

  17. Examples

  18. Writing an Equation

  19. Writing an Equation

  20. Writing an Equation

  21. Graphically solve each equation for

  22. Graphically solve each equation for

  23. ASSIGNMENT • Page 305 2-10 even, 11-18 all, 20-26 even • Test 8.1-8.3 Wednesday

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