text: 34
  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
  
  Citation preview
  
  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, )
explanation: The document is a detailed guide on graphing tangent and cotangent functions, including key points, transformations, and examples. It contains multiple questions that require the reader to fill in the blanks for amplitude, period, horizontal and vertical shifts, and key points for various tangent and cotangent functions.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: 34
  Graphing Tangent and Cotangent
  
  # Graphing Tangent and Cotangent
  
  efuru
  
  • View
  37
  
  6
  
  Embed Size (px)
  
  DESCRIPTION
  
  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
  
  Citation preview
  
  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, )
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is a detailed guide on graphing tangent and cotangent functions, including key points, transformations, and examples. It contains multiple questions that require the reader to fill in the blanks for amplitude, period, horizontal and vertical shifts, and key points for various tangent and cotangent functions.
  
  Label: multiple-question