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  Graphing Tangent and Cotangent
  
  # Graphing Tangent and Cotangent
  
  efuru
  
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  Graphing Tangent and Cotangent. Graphing Tangent Curve. 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. y = tan (x). Graphing Cotangent Curve. 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. y = cot (x). - PowerPoint PPT Presentation
  
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  Graphing Tangent and Cotangent
  
  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
  
  Graphing Cotangent Curvey = 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
  
  Using the Graphing CalculatorMode—
  
  • Window—– X min = - – X max = 3– X scale = /6
  
  • Window—– Y min =-3– Y max = 3– Y scale = .5
  
  Press Y=y1 = tan (x)
  
  y2 = 3tan (x)
  
  Press Graph
  
  Press Y=y1 = tan (x)
  
  y2 = 4tan (x)
  
  Press Graph
  
  Press Y=y1 = tan (x)
  
  y2 = -4tan (x)
  
  Press Graph
  
  Press Y=y1 = tan (x)
  
  y2 = tan (x) +1
  
  Press Graph
  
  Press Y=y1 = tan (x)
  
  y2 = tan (x +1)
  
  Press Graph
  
  Press Y=y1 = tan (x)
  
  y2 = tan (2x)
  
  Press Graph
  
  Press Y=y1 = tan (x)
  
  y2 = tan (1/2x)
  
  Press Graph
  
  Y = A tan (Bx - C) ± D
  
  No Amplitude,
  
  but determines two points
  
  on the graph.
  
  Period
  
  |B|
  
  Vertical Shift up/down
  
  Horizontal ShiftLeft/Right
  
  C B
  
  y = A tan (Bx – C) + D
  
  InterceptMaximum?AsymptoteMinimum?Intercept
  
  Unless A = Negative #InterceptMinimum?
  
  AsymptotesMaximum?Intercept
  
  Press Y=y1 = 1/tan (x)
  
  y2 = 3/tan (x)
  
  Press Graph
  
  y = cot (x)
  
  Press Y=y1 = 1/tan (x)
  
  y2 = 4/tan (x)
  
  Press Graph
  
  Press Y=y1 = 1/tan (x)
  
  y2 = -4/tan (x)
  
  Press Graph
  
  Press Y=y1 = 1/tan (x)
  
  y2 = 1/tan (x) +1
  
  Press Graph
  
  Press Y=y1 = 1/tan (x)
  
  y2 = 1/tan (x +1)
  
  Press Graph
  
  Press Y=y1 = 1/tan (x)
  
  y2 = 1/tan (2x)
  
  Press Graph
  
  Y = A cot (Bx - C) ± D
  
  Period |B|
  
  Vertical Shift up/down
  
  Horizontal ShiftLeft/Right
  
  C B
  
  No Amplitude,
  
  but determines two points
  
  on the graph.
  
  y = A cot (Bx – C) + D
  
  AsymptoteMaximum?InterceptMinimum?Asymptote
  
  Unless A = Negative #AsymptoteMinimum?Intercept
  
  Maximum?Asymptote
  
  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 = ________
  
  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 = ________
  
  Graphing by Key Pointsy = 2 tan x
  
  Amp = _________ Horizontal Shift = _______Period = _______ Vertical Shift = _________
  
  Inc. = ________
  
  (0, )(/4, )
  
  (/2, )
  
  (3/4, )
  
  (, )
  
  Graphing by Key Pointsy = -2 cot x
  
  Amp = _________ Horizontal Shift = _______Period = _______ Vertical Shift = _________
  
  Inc. = ________
  
  (0, )(/4, )
  
  (/2, )
  
  (3/4, )
  
  (, )
  
  Graphing by Key Pointsy = tan (1/2x)
  
  Amp = _________ Horizontal Shift = _______Period = _______ Vertical Shift = _________
  
  Inc. = ________
  
  (0, )(/2, )
  
  ( , )
  
  (3/2, )
  
  (2, )
  
  Graphing by Key Pointsy = 3 cot 1/2x
  
  Amp = _________ Horizontal Shift = _______Period = _______ Vertical Shift = _________
  
  Inc. = ________
  
  (0, )(/2, )
  
  (, )
  
  (3/2, )
  
  (2, )
  
  Graphing by Key Pointsy = 3 tan x +2
  
  Amp = _________ Horizontal Shift = _______Period = _______ Vertical Shift = _________
  
  Inc. = ________
  
  (0, )(/4 )
  
  (/2, )
  
  (3/4, )
  
  (, )
  
  Graphing by Key Pointsy = cot x - 2
  
  Amp = _________ Horizontal Shift = _______Period = _______ Vertical Shift = _________
  
  Inc. = ________
  
  (0, )(/4 )
  
  (/2, )
  
  (3/2, )
  
  (, )
  
  Graphing by Key Pointsy = -tan (x + )
  
  Amp = _________ Horizontal Shift = _______Period = _______ Vertical Shift = _________
  
  Inc. = ________
  
  (-, )(-3/4 , )
  
  (-/2 , )
  
  (-/4, )
  
  (0, )
  
  Graphing by Key Pointsy = cot (x - /4)
  
  Amp = _________ Horizontal Shift = _______Period = _______ Vertical Shift = _________
  
  Inc. = ________
  
  (/4 , )(/2, )
  
  (3/4, )
  
  (, )
  
  (5/4, )
  
  Graphing by Key Pointsy = 4tan (x/2 + /2)
  
  Amp = _________ Horizontal Shift = _______Period = _______ Vertical Shift = _________
  
  Inc. = ________
  
  (-, )(-/2 , )
  
  (0, )
  
  (/2, )
  
  (, )
  
  Graphing by Key Pointsy = -cot x
  
  Amp = _________ Horizontal Shift = _______Period = _______ Vertical Shift = _________
  
  Inc. = ________
  
  (0, )(1/4, )
  
  (1/2, )
  
  (3/4, )
  
  (1, )
  
  Graphing by Key Pointsy = 2tan (x/2 - /2) -1
  
  Amp = _________ Horizontal Shift = _______Period = _______ Vertical Shift = _________
  
  Inc. = ________
  
  (, )(3/2, )
  
  (2, )
  
  (5/2, )
  
  (3, )