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, )
The text passage is a PowerPoint presentation on graphing tangent and cotangent functions, including examples and key points for graphing. It contains multiple questions asking for the amplitude, period, horizontal and vertical shifts, and key points for various tangent and cotangent functions.
multiple_questions
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
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, )
user
The text passage is a PowerPoint presentation on graphing tangent and cotangent functions, including examples and key points for graphing. It contains multiple questions asking for the amplitude, period, horizontal and vertical shifts, and key points for various tangent and cotangent functions.

TYPE: MULTIPLE_QUESTIONS