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Transforming the Graph of sinx

Part 1 - Amplitude

The amplitude is the distance from any maximum or minimum to the axis of curve.

1. Neatly sketch the graphs of the functions listed below on the grid using different colours and label them clearly. The x-axis should have a scale from -360 to 360

2. Complete the following table.

|Function |Amplitude |

|y = sin(x) | |

|Y = 2sin(x) | |

|Y = 3sin(x) | |

3. How can you determine the amplitude from the equation?

______________________________________________________

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4. Graph y = - 3 sin(x). Sketch the graph on the grid and clearly label it.

a. Describe the change to the graph when y = 3sin(x) was changed to y = - 3 sin(x).

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b. Compare the amplitudes of y = 3sin(x) and y = - 3 sin(x). ___________

Part 2 - Period

The period of a periodic function is the length of one cycle, measured along the horizontal axis. Check your graph of y = sin(x) to confirm that the period is 3600.

1. Graph y = sin(x).

2. For y = sin(2x), what is the transformation from the graph of y = sin(x)?

3. Graph y = sin(2x)

4. What is the period of y = sin(2x)?________

5. For y = sin(4x), what is the transformation from the graph of y = sin(x)?

6. Graph y = sin(4x).

7. What is the period of y = sin(4x)? __________

8. Complete the following table.

|Function |Period |

|y = sin(x) | |

|y = sin(2x) | |

|y = sin(4x) | |

9. How can you determine the period from the equation?

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Part 3-Phase Shifts (Horizontal Shifts)

1. What is the transformation from y = sin(x) to y = sin(x + 900)?

2. Sketch the graph of y = sin(x) and

y = sin(x + 900) on the grid and clearly label them.

3. What is the transformation from y = sin(x) to y = sin(x - 1800)?

4. Sketch the graph of y = sin(x) and

y = sin(x - 1800) on the grid and clearly label them.

5. Complete the following table.

|Function |Phase Shift (Horizontal Shift) |

|y1 = sin(x) | |

|y2 = sin(x + 900) | |

|y3 = sin(x - 1800) | |

6. Explain how you can determine the phase shift from the equation.

_______________________________________________________

_______________________________________________________

Part 4 – Vertical Shifts

1. Neatly sketch the graphs below on the grid and label them clearly.

y = sin(x)

y = sin(x) + 2

y = sin(x) – 1

2. Complete the following table.

|Function |Vertical Shift |

|Y1 = sin(x) | |

|Y2 = sin(x) + 2 | |

|Y3 = sin(x) – 1 | |

3. Describe how you can determine the vertical shift from the equation.

_____________________________________________________

_____________________________________________________

Using your knowledge

1. Given the equation y = 3sin[2(( - 900)] + 2, predict the following:

Amplitude _______________

Period _________________

Phase Shift ________________

Vertical Shift ________________

2. Sketch the graph, shifting last.

Homework: pg. 309 C3, #1(don’t sketch) 2(don’t sketch), 3, 6, 7, 8a, 9, 11a)EOO

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