4.5: Graphing Sine and Cosine Functions

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• 4.5 Graphing Sine and Cosine Functions
• Objectives
• To recognize general shape of the graphs of
• sine and cosine functions
• - To determine the amplitude and period of the
  graphs
• To know how amplitude and period affect the
  graphs
• How to graph basic sine and cosine graphs
• Knowing how to determine a horizontal and
  vertical phase shifts
• Graphing sine and cosine graphs with horizontal
  and
• vertical shifts

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Now graph ysinx on the graph below using the
points above.
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Now do the same, but with cosine!
Now graph ycosx on the graph below using the
points above.
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Amplitude

• The amplitude of a trigonometric graph is
• ___________________________________
• What is the amplitude of the previously graphed
  trig functions? ____
• ? amplitude is always positive?
• How might you change the amplitude of a sine or
  cosine function???
• y a sin(x) or y a cos (x)
• Multiply the function by a constant!

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Graph the following

• y 2 cos(x)

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Period

• Period is __________________________
• The period of ysinx and ycosx is _____
• Why? _______________________________
• y a sin bx or y a cos bx
• Period 2__ Amplitude lal
• lbl

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Examples!

• Graph one cycle y sin(2x)
• Amp____ Period _______
• Sine functions start at (0,0), travel up to max,
  down through x-axis, down to minimum, back up to
  x-axis

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Another one! Yea!

• Graph y 3cos(½ x)

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• y -sinx What do you think happens?
• y -cosx

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Now Vertical Phase Shifts
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And, Horizontal Phase Shifts
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The basics of shifts.
Be very careful though..NOTICE that X has a
coefficient of one in the equation. If its not,
you must either factor the coefficient out or set
the factor equal to zero.
amp HPS per VPS
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More Examples

• List the amplitude, period, and phase shifts of
  the following

amp HPS per VPS
amp HPS per VPS
amp HPS per VPS
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All together now!
Graph
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Great- another one!

• Graph

HAPPY BIRTHDAY!!!