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0504 ch 5 day 4

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0504 ch 5 day 4

  1. 1. 5.3 Trigonometric GraphsMatthew 6:33 But seek first his kingdom and hisrighteousness, and all these things will be added unto you.
  2. 2. y = sin x
  3. 3. y = sin x } } } } Q1 Q2 Q3 Q4 Unit Circle
  4. 4. y = sin xMax: 1Min: -1 } } } } Q1 Q2 Q3 Q4 Unit Circle
  5. 5. y = sin xMax: 1Min: -1 max− minamplitude = =1 2 } } } } Q1 Q2 Q3 Q4 Unit Circle
  6. 6. y = sin xMax: 1Min: -1 max− minamplitude = =1 2 } } } }1 cycle occurs in 2π Q1 Q2 Q3 Q4∴ Period : 2π Unit Circle
  7. 7. y = sin xMax: 1Min: -1 max− minamplitude = =1 2 } } } }1 cycle occurs in 2π Q1 Q2 Q3 Q4∴ Period : 2π Unit CircleDomain : {x : x ∈R}Range : {y : −1 ≤ y ≤ 1}
  8. 8. y = sin xMax: 1Min: -1 max− minamplitude = =1 2 } } } }1 cycle occurs in 2π Q1 Q2 Q3 Q4∴ Period : 2π Unit CircleDomain : {x : x ∈R} Use the 5 key pointsRange : {y : −1 ≤ y ≤ 1} to help you graph
  9. 9. y = cos x
  10. 10. y = cos x } } } } Q1 Q2 Q3 Q4 Unit Circle Use the 5 key points to help you graph
  11. 11. y = cos xMax: 1Min: -1amplitude: 1Period: 2π } } } } Q1 Q2 Q3 Q4 Unit Circle Use the 5 key points to help you graph
  12. 12. y = cos xMax: 1Min: -1amplitude: 1Period: 2π } } } }Domain : {x : x ∈R} Q1 Q2 Q3 Q4Range : {y : −1 ≤ y ≤ 1} Unit Circle Use the 5 key points to help you graph
  13. 13. y = cos x Max: 1 Min: -1 amplitude: 1 Period: 2π } } } } Domain : {x : x ∈R} Q1 Q2 Q3 Q4 Range : {y : −1 ≤ y ≤ 1} Unit Circle πIf you shift cosθ right , Use the 5 key points 2it looks just like sin θ . to help you graph πThey are out of phase by . 2
  14. 14. y = cos x Max: 1 Min: -1 amplitude: 1 Period: 2π } } } } Domain : {x : x ∈R} Q1 Q2 Q3 Q4 Range : {y : −1 ≤ y ≤ 1} Unit Circle πIf you shift cosθ right , Use the 5 key points 2it looks just like sin θ . to help you graph πThey are out of phase by . 2 ⎛ π ⎞ sin θ = cos ⎜ θ − ⎟ ⎝ 2 ⎠
  15. 15. Sinusoidal Functions
  16. 16. Sinusoidal Functions y = asinb ( x − c ) + d
  17. 17. Sinusoidal Functions y = asinb ( x − c ) + d a is the amplitude if a < 0 , the graph is reflected about the x-axis
  18. 18. Sinusoidal Functions y = asinb ( x − c ) + d a is the amplitude if a < 0 , the graph is reflected about the x-axis b is related to the period in this way: normal period period = b
  19. 19. Sinusoidal Functions y = asinb ( x − c ) + d a is the amplitude if a < 0 , the graph is reflected about the x-axis b is related to the period in this way: normal period period = b c is the horizontal shift (or ‘phase shift’) if c < 0 , shifted left if c > 0 , shifted right
  20. 20. Sinusoidal Functions y = asinb ( x − c ) + d a is the amplitude if a < 0 , the graph is reflected about the x-axis b is related to the period in this way: normal period period = b c is the horizontal shift (or ‘phase shift’) if c < 0 , shifted left if c > 0 , shifted right d is the vertical shift
  21. 21. Discuss and Graph1. y = 3cosθ
  22. 22. Discuss and Graph1. y = 3cosθ amp : 3
  23. 23. Discuss and Graph1. y = 3cosθ amp : 3 per : 2π
  24. 24. Discuss and Graph1. y = 3cosθ amp : 3 per : 2π H .S. : none
  25. 25. Discuss and Graph1. y = 3cosθ amp : 3 per : 2π H .S. : none V.S. : none
  26. 26. Discuss and Graph1. y = 3cosθ amp : 3 per : 2π H .S. : none V.S. : noneKnow how to graph on trig graph paper using the5 key points. Verify with your calculator.
  27. 27. Discuss and Graph ⎛ π ⎞2. y = −2sin ⎜ x + ⎟ ⎝ 2 ⎠
  28. 28. Discuss and Graph ⎛ π ⎞2. y = −2sin ⎜ x + ⎟ ⎝ 2 ⎠ amp : 2
  29. 29. Discuss and Graph ⎛ π ⎞2. y = −2sin ⎜ x + ⎟ ⎝ 2 ⎠ amp : 2 per : 2π
  30. 30. Discuss and Graph ⎛ π ⎞2. y = −2sin ⎜ x + ⎟ ⎝ 2 ⎠ amp : 2 per : 2π π H .S. : left 2
  31. 31. Discuss and Graph ⎛ π ⎞2. y = −2sin ⎜ x + ⎟ ⎝ 2 ⎠ amp : 2 per : 2π π H .S. : left 2 V.S. : none
  32. 32. Discuss and Graph ⎛ π ⎞2. y = −2sin ⎜ x + ⎟ ⎝ 2 ⎠ amp : 2 per : 2π π H .S. : left 2 V.S. : none Reflected about the x-axis
  33. 33. Discuss and Graph3. y = sin ( 2x − π )
  34. 34. Discuss and Graph3. y = sin ( 2x − π ) Factor out the 2
  35. 35. Discuss and Graph3. y = sin ( 2x − π ) Factor out the 2 ⎛ π ⎞ y = sin 2 ⎜ x − ⎟ ⎝ 2 ⎠
  36. 36. Discuss and Graph3. y = sin ( 2x − π ) Factor out the 2 ⎛ π ⎞ y = sin 2 ⎜ x − ⎟ ⎝ 2 ⎠ amp : 1
  37. 37. Discuss and Graph3. y = sin ( 2x − π ) Factor out the 2 ⎛ π ⎞ y = sin 2 ⎜ x − ⎟ ⎝ 2 ⎠ amp : 1 per : π
  38. 38. Discuss and Graph3. y = sin ( 2x − π ) Factor out the 2 ⎛ π ⎞ y = sin 2 ⎜ x − ⎟ ⎝ 2 ⎠ amp : 1 norm. per. per : π period = b 2π p= =π 2
  39. 39. Discuss and Graph3. y = sin ( 2x − π ) Factor out the 2 ⎛ π ⎞ y = sin 2 ⎜ x − ⎟ ⎝ 2 ⎠ amp : 1 norm. per. per : π period = b π 2π H .S. : right p= =π 2 2
  40. 40. Discuss and Graph3. y = sin ( 2x − π ) Factor out the 2 ⎛ π ⎞ y = sin 2 ⎜ x − ⎟ ⎝ 2 ⎠ amp : 1 norm. per. per : π period = b π 2π H .S. : right p= =π 2 2 V.S. : none
  41. 41. Discuss and Graph 1 ⎛ 1 ⎞4. y = cos ⎜ x + π ⎟ − 1 2 ⎝ 2 ⎠
  42. 42. Discuss and Graph 1 ⎛ 1 ⎞4. y = cos ⎜ x + π ⎟ − 1 2 ⎝ 2 ⎠ 1 1 y = cos ( x + 2π ) − 1 2 2
  43. 43. Discuss and Graph 1 ⎛ 1 ⎞4. y = cos ⎜ x + π ⎟ − 1 2 ⎝ 2 ⎠ 1 1 y = cos ( x + 2π ) − 1 2 2 1 amp : 2
  44. 44. Discuss and Graph 1 ⎛ 1 ⎞4. y = cos ⎜ x + π ⎟ − 1 2 ⎝ 2 ⎠ 1 1 y = cos ( x + 2π ) − 1 2 2 1 amp : 2 per : 4π
  45. 45. Discuss and Graph 1 ⎛ 1 ⎞4. y = cos ⎜ x + π ⎟ − 1 2 ⎝ 2 ⎠ 1 1 y = cos ( x + 2π ) − 1 2 2 1 amp : norm. per. 2 period = b per : 4π 2π p= = 4π 1 2
  46. 46. Discuss and Graph 1 ⎛ 1 ⎞4. y = cos ⎜ x + π ⎟ − 1 2 ⎝ 2 ⎠ 1 1 y = cos ( x + 2π ) − 1 2 2 1 amp : norm. per. 2 period = b per : 4π 2π p= = 4π H .S. : 2π left 1 2
  47. 47. Discuss and Graph 1 ⎛ 1 ⎞4. y = cos ⎜ x + π ⎟ − 1 2 ⎝ 2 ⎠ 1 1 y = cos ( x + 2π ) − 1 2 2 1 amp : norm. per. 2 period = b per : 4π 2π p= = 4π H .S. : 2π left 1 2 V.S. : 1 down
  48. 48. Discuss and Graph 1 ⎛ 1 ⎞4. y = cos ⎜ x + π ⎟ − 1 2 ⎝ 2 ⎠ 1 1 y = cos ( x + 2π ) − 1 2 2 1 amp : norm. per. 2 period = b per : 4π 2π p= = 4π H .S. : 2π left 1 2 V.S. : 1 down Use the 5 key points to help you graph this!
  49. 49. HW #4Unless you’re willing to have a go, fail miserably,and have another go, success won’t happen. Phillip Adams

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