Graphing cosecant and secant
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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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Graphing cosecant and secant

Graphing Cosecant and Secant


Using the graphing calculator

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

Press Y=

  • y1 = sin (x)

  • y2 = 1/sin (x)

Press Graph


Press y1

Press Y=

  • y1 = 3sin (X)

  • y2 = 3/sin(x)

Press Graph


Press y2

Press Y=

  • y1 = sin (X) + 1

  • y2 = 1/sin (X) +1

Press Graph


Press y3

Press Y=

  • y1 = sin (x + 1)

  • y2 = 1/sin (x +1)

Press Graph


Press y4

Press Y=

  • y1 = sin (2x)

  • y2 = 1/sin (2x)

Press Graph


Graphing cosecant and secant

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.


Graphing cosecant and secant

What do you think the secant curve will look like?

  • Check out your thoughts by …

Press Y=

  • y1 = cos (x)

  • y2 = 1/cos (x)


Graphing cosecant and secant

So, let’s graph cosecant and secant graphs.


Graphing cosecant curve

Graphing Cosecant 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 = csc (x)


Graphing cosine curve

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)


Graphing cosecant and secant

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


Graphing by key points

Graphing by Key Points

  • y = 2 csc x Think: ____________________

    Amp = _________ Horizontal Shift = _______

    Period = _______ Vertical Shift = _________

    Inc. = ______

(0, )

(/2, )

(, )

(3/2, )

(2, )


Graphing cosecant and secant

Graphing by Key Points

  • y = -2 sec x Think: ____________________

    Amp = _________ Horizontal Shift = _______

    Period = _______ Vertical Shift = _________

    Inc. = ______

(0, )

(/2, )

(, )

(3/2, )

(2, )


Graphing cosecant and secant

Graphing by Key Points

  • y = sec 4x Think: ____________________

    Amp = _________ Horizontal Shift = _______

    Period = _______ Vertical Shift = _________

    Inc. = ______

(0, )

(/8, )

(/4, )

(3/8, )

(/2, )


Graphing cosecant and secant

Graphing by Key Points

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

    Amp = _________ Horizontal Shift = _______

    Period = _______ Vertical Shift = _________

    Inc. = _____

(0, )

(, )

(2, )

(3, )

(4, )


Graphing cosecant and secant

Graphing by Key Points

  • y = 3 sec x +2 Think: ____________________

    Amp = _________ Horizontal Shift = _______

    Period = _______ Vertical Shift = _________

    Inc. = ______

(0, )

(/2 )

(, )

(3/2, )

(2, )


Graphing cosecant and secant

Graphing by Key Points

  • y = sec x +2 Think: ____________________

    Amp = _________ Horizontal Shift = _______

    Period = _______ Vertical Shift = _________

    Inc. = ______

(0, )

(/2 )

(, )

(3/2, )

(2, )


Graphing cosecant and secant

Graphing by Key Points

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

    Amp = _________ Horizontal Shift = _______

    Period = _______ Vertical Shift = _________

    Inc. = ______

(-, )

(-/2 )

(0, )

(/2, )

(, )


Graphing cosecant and secant

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 cosecant and secant

Graphing by Key Points

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

    Amp = _________ Horizontal Shift = _______

    Period = _______ Vertical Shift = _________

    Inc. = ______

(, )

(2, )

(3, )

(4, )

(5, )


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