# Graphing Cosecant and Secant - PowerPoint PPT Presentation

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Graphing Cosecant and Secant. Using the Graphing Calculator. Mode— Radians Function Sequential. Window— X min = -  X max = 3 X scale = /6. Window— Y min =-5 Y max = 5 Y scale = .5. Press Y=. y 1 = sin (x) y 2 = 1/sin (x). Press Graph. Press Y=. y 1 = 3sin (X)

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Graphing Cosecant and Secant

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### Using the Graphing Calculator

• Mode—

• Function

• Sequential

• Window—

• X min = - 

• X max = 3

• X scale = /6

• Window—

• Y min =-5

• Y max = 5

• Y scale = .5

### Press Y=

• y1 = sin (x)

• y2 = 1/sin (x)

Press Graph

### Press Y=

• y1 = 3sin (X)

• y2 = 3/sin(x)

Press Graph

### Press Y=

• y1 = sin (X) + 1

• y2 = 1/sin (X) +1

Press Graph

### Press Y=

• y1 = sin (x + 1)

• y2 = 1/sin (x +1)

Press Graph

### Press Y=

• y1 = sin (2x)

• y2 = 1/sin (2x)

Press Graph

What are you noticing???

• The only points that the two curves have in common are the maxima and minima of the sine curve.

• The cosecant curve has asymptotes at the intercepts of the sine curve.

• The cosecant curve is just a series of parabola shaped graphs that alternate opening up and then down.

What do you think the secant curve will look like?

• Check out your thoughts by …

Press Y=

• y1 = cos (x)

• y2 = 1/cos (x)

So, let’s graph cosecant and secant graphs.

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 = csc (x)

### Graphing Cosine 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 =sec(x)

So, let’s graph cosecant and secant graphs with key points.

### Graphing by Key Points

• y = 2 csc x Think: ____________________

Amp = _________ Horizontal Shift = _______

Period = _______ Vertical Shift = _________

Inc. = ______

(0, )

(/2, )

(, )

(3/2, )

(2, )

Graphing by Key Points

• y = -2 sec x Think: ____________________

Amp = _________ Horizontal Shift = _______

Period = _______ Vertical Shift = _________

Inc. = ______

(0, )

(/2, )

(, )

(3/2, )

(2, )

Graphing by Key Points

• y = sec 4x Think: ____________________

Amp = _________ Horizontal Shift = _______

Period = _______ Vertical Shift = _________

Inc. = ______

(0, )

(/8, )

(/4, )

(3/8, )

(/2, )

Graphing by Key Points

• y = 3 csc 1/2x Think: ____________________

Amp = _________ Horizontal Shift = _______

Period = _______ Vertical Shift = _________

Inc. = _____

(0, )

(, )

(2, )

(3, )

(4, )

Graphing by Key Points

• y = 3 sec x +2 Think: ____________________

Amp = _________ Horizontal Shift = _______

Period = _______ Vertical Shift = _________

Inc. = ______

(0, )

(/2 )

(, )

(3/2, )

(2, )

Graphing by Key Points

• y = sec x +2 Think: ____________________

Amp = _________ Horizontal Shift = _______

Period = _______ Vertical Shift = _________

Inc. = ______

(0, )

(/2 )

(, )

(3/2, )

(2, )

Graphing by Key Points

• y = csc (x + ) Think: ____________________

Amp = _________ Horizontal Shift = _______

Period = _______ Vertical Shift = _________

Inc. = ______

(-, )

(-/2 )

(0, )

(/2, )

(, )

Graphing by Key Points

• y = sec (x - /4) Think: ____________________

Amp = _________ Horizontal Shift = _______

Period = _______ Vertical Shift = _________

Inc. = ______

(/4 , )

(3/4, )

(5/4, )

(7/4, )

(9/4, )

Graphing by Key Points

• y = 2 sec (x/2 - /2) -1 Think: ________________

Amp = _________ Horizontal Shift = _______

Period = _______ Vertical Shift = _________

Inc. = ______

(, )

(2, )

(3, )

(4, )

(5, )