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 y
2
= sin (x)
= 1/sin (x)
Press Graph

Press Y=

 y
1 y
2
= 3sin (X)
= 3/sin(x)
Press Graph

Press Y=

 y
1 y
2
= sin (X) + 1
= 1/sin (X) +1
Press Graph

Press Y=

 y
1 y
2
= sin (x + 1)
= 1/sin (x +1)
Press Graph

Press Y=

 y
1 y
2
= sin (2x)
= 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=

 y
1 y
2
= cos (x)
= 1/cos (x)

So, let’s graph cosecant and secant graphs.

0
Graphing Cosecant Curve
 y = csc (x)
5  /6

7  /6
5  /4
4  /3
3  /2
 /6
 /4
 /3
 /2
2  /3
3  /4
5  /3
7  /4
11  /6
2 

0
Graphing Cosine Curve
 y =sec(x)
5  /6

7  /6
5  /4
4  /3
3  /2
 /6
 /4
 /3
 /2
2  /3
3  /4
5  /3
7  /4
11  /6
2 

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 /
2 x 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  , )