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Published byLizette Normandy Modified over 2 years ago

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Graphing Tangent and Cotangent

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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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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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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= y 1 = tan (x) y 2 = 3tan (x) Press Graph

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Press Y= y 1 = tan (x) y 2 = 4tan (x) Press Graph

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Press Y= y 1 = tan (x) y 2 = -4tan (x) Press Graph

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Press Y= y 1 = tan (x) y 2 = tan (x) +1 Press Graph

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Press Y= y 1 = tan (x) y 2 = tan (x +1) Press Graph

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Press Y= y 1 = tan (x) y 2 = tan (2x) Press Graph

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Press Y= y 1 = tan (x) y 2 = tan (1/2x) Press Graph

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Y = A tan (Bx - C) ± D No Amplitude, but determines two points on the graph. Period |B| Vertical Shift up/down 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? Asymptotes Maximum? Intercept

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Press Y= y 1 = 1/tan (x) y 2 = 3/tan (x) Press Graph y = cot (x)

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Press Y= y 1 = 1/tan (x) y 2 = 4/tan (x) Press Graph

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Press Y= y 1 = 1/tan (x) y 2 = -4/tan (x) Press Graph

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Press Y= y 1 = 1/tan (x) y 2 = 1/tan (x) +1 Press Graph

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Press Y= y 1 = 1/tan (x) y 2 = 1/tan (x +1) Press Graph

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Press Y= y 1 = 1/tan (x) y 2 = 1/tan (2x) Press Graph

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Y = A cot (Bx - C) ± D Period |B| Vertical Shift up/down Horizontal Shift Left/Right C B No Amplitude, but determines two points on the graph.

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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 / 2 x 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 , )

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