Graphing Tangent and Cotangent

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Graphing Tangent and Cotangent
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Using the Graphing Calculator

• Mode
• Radians
• Function
• Sequential

• Window
• X min - ?
• X max 3?
• X scale ?/6

• Window
• Y min -3
• Y max 3
• Y scale .5

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Press Y

• y1 tan (x)
• y2 3tan (x)

Press Graph
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Press Y

• y1 tan (x)
• y2 4tan (x)

Press Graph
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Press Y

• y1 tan (x)
• y2 -4tan (x)

Press Graph
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Press Y

• y1 tan (x)
• y2 tan (x) 1

Press Graph
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Press Y

• y1 tan (x)
• y2 tan (x 1)

Press Graph
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Press Y

• y1 tan (x)
• y2 tan (2x)

Press Graph
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Press Y

• y1 tan (x)
• y2 tan (1/2x)

Press Graph
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Graphing Tangent Curve

• y tan (x)

0 ?/6 ?/4 ?/3 ?/2 2?/3 3?/4 5?/6 ? 7?/6 5?/4 4?/3
3?/2 5?/3 7?/4 11?/6 2?
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• Y A tan (Bx - C) D

Vertical Shift up/down
Period ? B
No Amplitude, but determines two points on the
graph.
Horizontal Shift Left/Right C
B
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y A tan (Bx C) D
Intercept Maximum? Asymptote Minimum? Intercept
Unless A Negative Intercept Minimum? Asymptote
s Maximum? Intercept
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Press Y
y cot (x)

• y1 1/tan (x)
• y2 3/tan (x)

Press Graph
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Press Y

• y1 1/tan (x)
• y2 4/tan (x)

Press Graph
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Press Y

• y1 1/tan (x)
• y2 -4/tan (x)

Press Graph
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Press Y

• y1 1/tan (x)
• y2 1/tan (x) 1

Press Graph
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Press Y

• y1 1/tan (x)
• y2 1/tan (x 1)

Press Graph
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Press Y

• y1 1/tan (x)
• y2 1/tan (2x)

Press Graph
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Graphing Cotangent Curve

• y cot (x)

0 ?/6 ?/4 ?/3 ?/2 2?/3 3?/4 5?/6 ? 7?/6 5?/4 4?/3
3?/2 5?/3 7?/4 11?/6 2?
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• Y A cot (Bx - C) D

Vertical Shift up/down
Period ? B
No Amplitude, but determines two points on the
graph.
Horizontal Shift Left/Right C
B
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y A cot (Bx C) D
Asymptote Maximum? Intercept Minimum? Asymptote
Unless A Negative Asymptote Minimum? Intercept
Maximum? Asymptote
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Examples--

• y 3tan (x 1) -3
• Amp. _______
• Period _____
• Horizontal Phase Shift _________
• Vertical Phase Shift ________

• y cot (x - 2)
• Amp. _______
• Period _____
• Horizontal Phase Shift _________
• Vertical Phase Shift ________

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• y cot (2x)
• Amp. _______
• Period _____
• Horizontal Phase Shift _________
• Vertical Phase Shift ________

• y ½ tan (½ x) 1
• Amp. _______
• Period _____
• Horizontal Phase Shift _________
• Vertical Phase Shift ________

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Graphing by Key Points

• y 2 tan x
• Amp _________ Horizontal Shift _______
• Period _______ Vertical Shift
  _________
• Inc. ________

• (0, )

• (?/4, )

• (?/2, )

• (3?/4, )

• (?, )

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Graphing by Key Points

• y -2 cot x
• Amp _________ Horizontal Shift _______
• Period _______ Vertical Shift
  _________
• Inc. ________

• (0, )

• (?/4, )

• (?/2, )

• (3?/4, )

• (?, )

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Graphing by Key Points

• y tan (1/2x)
• Amp _________ Horizontal Shift _______
• Period _______ Vertical Shift
  _________
• Inc. ________

• (0, )

• (?/2, )

• (? , )

• (3?/2, )

• (2?, )

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Graphing by Key Points

• y 3 cot 1/2x
• Amp _________ Horizontal Shift _______
• Period _______ Vertical Shift
  _________
• Inc. ________

• (0, )

• (?/2, )

• (?, )

• (3?/2, )

• (2?, )

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Graphing by Key Points

• y 3 tan x 2
• Amp _________ Horizontal Shift _______
• Period _______ Vertical Shift
  _________
• Inc. ________

• (0, )

• (?/4 )

• (?/2, )

• (3?/4, )

• (?, )

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Graphing by Key Points

• y cot x - 2
• Amp _________ Horizontal Shift _______
• Period _______ Vertical Shift
  _________
• Inc. ________

• (0, )

• (?/4 )

• (?/2, )

• (3?/2, )

• (?, )

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Graphing by Key Points

• y -tan (x ?)
• Amp _________ Horizontal Shift _______
• Period _______ Vertical Shift
  _________
• Inc. ________

• (-?, )

• (-3?/4 , )

• (-?/2 , )

• (-?/4, )

• (0, )

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Graphing by Key Points

• y cot (x - ?/4)
• Amp _________ Horizontal Shift _______
• Period _______ Vertical Shift
  _________
• Inc. ________

• (?/4 , )

• (?/2, )

• (3?/4, )

• (?, )

• (5?/4, )

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Graphing by Key Points

• y 4tan (x/2 ?/2)
• Amp _________ Horizontal Shift _______
• Period _______ Vertical Shift
  _________
• Inc. ________

• (-?, )

• (-?/2 , )

• (0, )

• (?/2, )

• (?, )

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Graphing by Key Points

• y -cot ?x
• Amp _________ Horizontal Shift _______
• Period _______ Vertical Shift
  _________
• Inc. ________

• (0, )

• (1/4, )

• (1/2, )

• (3/4, )

• (1, )

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Graphing by Key Points

• y 2tan (x/2 - ?/2) -1
• Amp _________ Horizontal Shift _______
• Period _______ Vertical Shift
  _________
• Inc. ________

• (?, )

• (3?/2, )

• (2?, )

• (5?/2, )

• (3?, )