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Graphing Tangent and Cotangent

Graphing Tangent and Cotangent

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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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Page 1: Graphing  Tangent and Cotangent

Graphing Tangent and Cotangent

Page 2: 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

Page 3: Graphing  Tangent and Cotangent

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

Page 4: Graphing  Tangent and Cotangent

Using the Graphing CalculatorMode—

RadiansFunctionSequential

• Window—– X min = - – X max = 3– X scale = /6

• Window—– Y min =-3– Y max = 3– Y scale = .5

Page 5: Graphing  Tangent and Cotangent

Press Y=y1 = tan (x)

y2 = 3tan (x)

Press Graph

Page 6: Graphing  Tangent and Cotangent

Press Y=y1 = tan (x)

y2 = 4tan (x)

Press Graph

Page 7: Graphing  Tangent and Cotangent

Press Y=y1 = tan (x)

y2 = -4tan (x)

Press Graph

Page 8: Graphing  Tangent and Cotangent

Press Y=y1 = tan (x)

y2 = tan (x) +1

Press Graph

Page 9: Graphing  Tangent and Cotangent

Press Y=y1 = tan (x)

y2 = tan (x +1)

Press Graph

Page 10: Graphing  Tangent and Cotangent

Press Y=y1 = tan (x)

y2 = tan (2x)

Press Graph

Page 11: Graphing  Tangent and Cotangent

Press Y=y1 = tan (x)

y2 = tan (1/2x)

Press Graph

Page 12: Graphing  Tangent and Cotangent

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

Page 13: Graphing  Tangent and Cotangent

y = A tan (Bx – C) + D

InterceptMaximum?AsymptoteMinimum?Intercept

Unless A = Negative #InterceptMinimum?

AsymptotesMaximum?Intercept

Page 14: Graphing  Tangent and Cotangent

Press Y=y1 = 1/tan (x)

y2 = 3/tan (x)

Press Graph

y = cot (x)

Page 15: Graphing  Tangent and Cotangent

Press Y=y1 = 1/tan (x)

y2 = 4/tan (x)

Press Graph

Page 16: Graphing  Tangent and Cotangent

Press Y=y1 = 1/tan (x)

y2 = -4/tan (x)

Press Graph

Page 17: Graphing  Tangent and Cotangent

Press Y=y1 = 1/tan (x)

y2 = 1/tan (x) +1

Press Graph

Page 18: Graphing  Tangent and Cotangent

Press Y=y1 = 1/tan (x)

y2 = 1/tan (x +1)

Press Graph

Page 19: Graphing  Tangent and Cotangent

Press Y=y1 = 1/tan (x)

y2 = 1/tan (2x)

Press Graph

Page 20: Graphing  Tangent and Cotangent

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.

Page 21: Graphing  Tangent and Cotangent

y = A cot (Bx – C) + D

AsymptoteMaximum?InterceptMinimum?Asymptote

Unless A = Negative #AsymptoteMinimum?Intercept

Maximum?Asymptote

Page 22: Graphing  Tangent and Cotangent

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 = ________

Page 23: Graphing  Tangent and Cotangent

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 = ________

Page 24: Graphing  Tangent and Cotangent

Graphing by Key Pointsy = 2 tan x

Amp = _________ Horizontal Shift = _______Period = _______ Vertical Shift = _________

Inc. = ________

(0, )(/4, )

(/2, )

(3/4, )

(, )

Page 25: Graphing  Tangent and Cotangent

Graphing by Key Pointsy = -2 cot x

Amp = _________ Horizontal Shift = _______Period = _______ Vertical Shift = _________

Inc. = ________

(0, )(/4, )

(/2, )

(3/4, )

(, )

Page 26: Graphing  Tangent and Cotangent

Graphing by Key Pointsy = tan (1/2x)

Amp = _________ Horizontal Shift = _______Period = _______ Vertical Shift = _________

Inc. = ________

(0, )(/2, )

( , )

(3/2, )

(2, )

Page 27: Graphing  Tangent and Cotangent

Graphing by Key Pointsy = 3 cot 1/2x

Amp = _________ Horizontal Shift = _______Period = _______ Vertical Shift = _________

Inc. = ________

(0, )(/2, )

(, )

(3/2, )

(2, )

Page 28: Graphing  Tangent and Cotangent

Graphing by Key Pointsy = 3 tan x +2

Amp = _________ Horizontal Shift = _______Period = _______ Vertical Shift = _________

Inc. = ________

(0, )(/4 )

(/2, )

(3/4, )

(, )

Page 29: Graphing  Tangent and Cotangent

Graphing by Key Pointsy = cot x - 2

Amp = _________ Horizontal Shift = _______Period = _______ Vertical Shift = _________

Inc. = ________

(0, )(/4 )

(/2, )

(3/2, )

(, )

Page 30: Graphing  Tangent and Cotangent

Graphing by Key Pointsy = -tan (x + )

Amp = _________ Horizontal Shift = _______Period = _______ Vertical Shift = _________

Inc. = ________

(-, )(-3/4 , )

(-/2 , )

(-/4, )

(0, )

Page 31: Graphing  Tangent and Cotangent

Graphing by Key Pointsy = cot (x - /4)

Amp = _________ Horizontal Shift = _______Period = _______ Vertical Shift = _________

Inc. = ________

(/4 , )(/2, )

(3/4, )

(, )

(5/4, )

Page 32: Graphing  Tangent and Cotangent

Graphing by Key Pointsy = 4tan (x/2 + /2)

Amp = _________ Horizontal Shift = _______Period = _______ Vertical Shift = _________

Inc. = ________

(-, )(-/2 , )

(0, )

(/2, )

(, )

Page 33: Graphing  Tangent and Cotangent

Graphing by Key Pointsy = -cot x

Amp = _________ Horizontal Shift = _______Period = _______ Vertical Shift = _________

Inc. = ________

(0, )(1/4, )

(1/2, )

(3/4, )

(1, )

Page 34: Graphing  Tangent and Cotangent

Graphing by Key Pointsy = 2tan (x/2 - /2) -1

Amp = _________ Horizontal Shift = _______Period = _______ Vertical Shift = _________

Inc. = ________

(, )(3/2, )

(2, )

(5/2, )

(3, )