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) y 2 = 3/sin(x) Press Graph

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

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

Press Y= y 1 = sin (2x) y 2 = 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 = cos (x) y 2 = 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 Curve y =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 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 , )