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Graphing Cosecant and Secant

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- Mode—
- Radians
- Function
- Sequential

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

- Window—
- Y min =-5
- Y max = 5
- Y scale = .5

- y1 = sin (x)
- y2 = 1/sin (x)

Press Graph

- y1 = 3sin (X)
- y2 = 3/sin(x)

Press Graph

- y1 = sin (X) + 1
- y2 = 1/sin (X) +1

Press Graph

- y1 = sin (x + 1)
- y2 = 1/sin (x +1)

Press Graph

- 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)

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.

- 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, )