Graphs of Sine and Cosine Functions

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Graphs of Sine and Cosine Functions. Section 4.5. Fast Wave, Slow Wave. Who cares about waves??. Create the sine and cosine Graphs. Creating the Graphs. sine and cosine graphs. Sine graph plotted Cosine graph plotted. What about negative values?. Does the graph repeat? When?. - PowerPoint PPT Presentation

Transcript of Graphs of Sine and Cosine Functions

  • Graphs of Sine and Cosine FunctionsSection 4.5

  • Fast Wave, Slow Wave

    Who cares about waves??

  • Create the sine and cosine Graphs

    Creating the Graphs

    Angle ValueSineCosine0 (0 radians)0130 (/6 radians)3/245 (/4 radians)2/22/260 (/3 radians)3/21/290 (/2 radians)10 135 (3/4 radians)2/2-2/2180 ( radians)0-1270 (3/2 radians)-10360 (2 radians)01450 (5/2 radians)-10540 (2 radians)0-1630 (2 radians)-10720 (2 radians)01

  • sine and cosine graphs

    Sine graph plotted Cosine graph plotted

  • What about negative values?

  • Does the graph repeat?

    When?

    One complete cycle of the cosine and sine graphs is called the ___period___

  • Key PointsWhat did you find???

    Key Points

    What are key points? What do they mean?

  • Review Graphing sine and cosineWhere do they graphs come from?!?

    Graphing Sine and Cosine Review

    graphing sine and cosine - radians

  • Listing the Key PointsSinx:(0,0) (90, 1) (180,0) (270, -1) (360, 0)

    Cosx:(0,1) (90,0) (180, -1) (270, 0) (360, -1)

  • Transformations to the parent graphs sine and cosineWe will see how transformations affect the basic sine and cosine parent graphs

  • General Equations:y = asin(bx c) + d

    y = acos(bx c) + d

  • Vertical TranslationsA vertical shift is the vertical distance between the midline of the graph and the x axis.

    For y = sinx +d and y = cosx +d, the constant d causes a vertical shift in the graph

    Which value (x or y) is influenced by the change in the d value?

  • Whats Happening?? Transformations of Sine and Cosine

  • Vertical Translations

    The shift is d units upward for d >0

    The shift is d units downward for d< 0

    The graph oscillates about line y = d instead of x-axis

    Does the period change when d changes?

  • Examples:

  • AmplitudeThe amplitude of y = asinx and y = acosx represents the vertical distance between the midline and the maximum or minimum

    Amplitude = |a|

    The constant factor a is a scaling factor - a vertical stretch or shrink of the basic sine and cosine curves

  • Whats Happening?? Transformations of Sine and Cosine

  • AmplitudeWhat Does It Do??If a 1, the basic sine curve is stretched vertically

    If a -1, the basic sine curve is reflected across the x-axis and vertically stretched

    The graph of y = asinx ranges between -a and a instead of between -1 and 1

  • AmplitudeWhat Does It Do??If 0
  • Examples:

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