GRAPHING TRIGONOMETRIC FUNCTIONS

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GRAPHING TRIGONOMETRIC FUNCTIONS

• Using the TI-83
• Eastern High School
• July, 2007

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GRAPHING BASIC TRIGONOMETRIC FUNCTIONS

• Setting up the calculator.
• Graphing the sine and cosine functions.
• Graphing the tangent
• function.
• Graphing the reciprocal trig functions.

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Setting Up the Calculator

• Press the Mode key.
• Select the appropriate mode.
• Press Window key.
• Choose your x-min value and x-max value.
• Use the pi or p key when appropriate.
• Set your x-scale by using ¼ of the length of the
  period.

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Graphing Sine and Cosine Curves in the form y a
sin(bx) y a cos(bx)

• Choosing the Ymin and Ymax values depends on the
  amplitude. Find the amplitude, l a l.
• It is recommended to select a Ymin at least one
  value lower than your amplitude (plus the phase
  shift) and to select a Ymax at least one value
  higher than that value. Select an appropriate
  y-scl based on the size of your amplitude. A 1
  value will probably be sufficient.
• Leave Xres 1.

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Viewing the Graph

• Press the y key.
• Check to be sure the Plot 1 key is not
  highlighted.
• Enter the equation under Y1.
• Press the graph key.

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SAMPLE GRAPH y 3 sin(2x)

• For y 3 sin (2x), the amplitude 3 and the
  period is (2p)/2 or p.
• Setting The Window
• In order to graph 2 full cycles, set the Xmin at
  p and the Xmax at p.
• Since the period is p, the Xscl should be ¼ of p,
  or p/4.
• Since the amplitude is 3, set the Ymin -4, the
  Ymax 4, and Yscl1.
• Enter the equation in Y1

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Graphing the tangent curve in the form of y a
tan (bx)

• The window setting for x min and x max should be
  set according to the number of cycles desired.
  Again, the x sc l should be set to ¼ of the
  period. Recall the period of the tangent function
  is p/ lbl
• Since the tangent function has no upper and lower
  limit, choose a reasonable y min and y max value
  for the window setting. Be sure to include values
  at least from a to a.

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SAMPLE GRAPH y 2 tan x

• For y 2 tan x, a 2 and the period is p/1, or
  p.
• Setting the window
• Since the period is p, the Xmin should be set at
  p, the Xmax is p, and the Xscl should be set to
  p/4.
• Since a 2, set the Ymin to -5, Ymax to 5, and
  the Yscl to 1.
• Enter the equation in Y1.

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GRAPHING THE RECIPROCAL FUNCTIONS

• In order to graph the reciprocal trig functions,
  use the reciprocal key x-1 with either the sin,
  cos, or tan key.

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SAMPLE PROBLEM y 2sec x

• Since the secant is the reciprocal of cosine,
  consider the graph of y 2 cos x when setting
  the Xmin, Xmax and Xscl on the window. Since the
  period is 2p, set the xscl
• Xmin -2p Xmax 2p Xscl p/2
• Since the secant has no limit, set the Ymin lower
  than l a l and Ymax higher than la l.
• Ymin- 6 and Ymax 6.
• Enter the equation in Y1.

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The graph of y 2 sec x

• The graph of y 2 sec x is shown here. Do you
  see the asymptotes? Are there any x or y-
  intercepts?

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Now, try these! Graph at least two cycles.

• y 3 csc 4x.
• y 5 cot 2x.
• y 2 cos ¼x.
• y -4 sin px
• y ½ tan x.
• y -3 sec x/2

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1) y 3csc(4x) 2) y5cot (2x)
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3) y 2 cos ¼x 4) y-4sinpx
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5) y ½ tan x 6) y - 3sec x/2