Graphing Cosecant and Secant

Using the Graphing CalculatorMode—

RadiansFunctionSequential

• 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.

Graphing Cosecant Curve 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

Graphing Cosine Curvey =sec(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

So, let’s graph cosecant and secant graphs

with key points.

Graphing by Key Pointsy = 2 csc x Think: ____________________

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

Inc. = ______

(0, )(/2, )

(, )

(3/2, )

(2, )

Graphing by Key Pointsy = -2 sec x Think: ____________________

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

Inc. = ______

(0, )(/2, )

(, )

(3/2, )

(2, )

Graphing by Key Pointsy = sec 4x Think: ____________________

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

Inc. = ______

(0, )(/8, )

(/4, )

(3/8, )

(/2, )

Graphing by Key Pointsy = 3 csc 1/2x Think: ____________________

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

Inc. = _____

(0, )(, )

(2, )

(3, )

(4, )

Graphing by Key Pointsy = 3 sec x +2 Think: ____________________

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

Inc. = ______

(0, )(/2 )

(, )

(3/2, )

(2, )

Graphing by Key Pointsy = sec x +2 Think: ____________________

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

Inc. = ______

(0, )(/2 )

(, )

(3/2, )

(2, )

Graphing by Key Pointsy = csc (x + ) Think: ____________________

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

Inc. = ______

(-, )(-/2 )

(0, )

(/2, )

(, )

Graphing by Key Pointsy = sec (x - /4) Think: ____________________

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

Inc. = ______

(/4 , )(3/4, )

(5/4, )

(7/4, )

(9/4, )

Graphing by Key Pointsy = 2 sec (x/2 - /2) -1 Think: ________________

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

Inc. = ______

(, )(2, )

(3, )

(4, )

(5, )