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## Graphing Cosecant and Secant

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**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=**• 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)**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**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 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 1/2x 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, )