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3.1 Sinusoids

3.1 Sinusoids. Lesson Objective: Iwbat to understand amplitude, period, cycle, & phase displacement of a sinusoid. Guiding Question: What are all the ways we can manipulate a graph?. Sine Parent function: y= sinx. Cosine Parent Function y = cosx.

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3.1 Sinusoids

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  1. 3.1 Sinusoids Lesson Objective: Iwbat to understand amplitude, period, cycle, & phase displacement of a sinusoid.

  2. Guiding Question: What are all the ways we can manipulate a graph? Sine Parent function: y=sinx Cosine Parent Function y = cosx

  3. Guiding Question: What are all the ways we can manipulate a graph? • Recall how to manipulate any function Where a & d manipulate vertically and b & c manipulate horizontally.

  4. Guiding Question: What are all the ways we can manipulate a graph? • Period – how long to go one cycle (horizontal dilation) • Amplitude – how high/low you go. (vertical dilation) • Parent sin/cosfcns • Period: 360 degrees • Amplitude 1 unit

  5. Guiding Question: What are all the ways we can manipulate a graph? • Phase displacement – (horizontal translation) move the graph horizontally by a degree measure

  6. Guiding Question: What are all the ways we can manipulate a graph? • Vertical Translation – Moves the entire graph (sinusoidal axis) up/down

  7. Guiding Question: What are all the ways we can manipulate a graph? • Ways to manipulate a trig function (Cos is same) A = Amplitude (vertical dilation) B = reciprocal of horizontal dilation ( C = Location of sinusoidal axis (vert. translation) D = Phase displacement (horizontal translation)

  8. Guiding Question: What are all the ways we can manipulate a graph? • What do you notice about the period between 1 and 2? • What does #3 do? • What does #4 do? • On a calculator graph. • Y = sin x • Y = sin (4x) • Y = sin (x) + 4 • Y = sin (x – 30)

  9. Guiding Question: What are all the ways we can manipulate a graph? • Assignment: Pg. 95-96 1-9

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