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Graphing Cosecant and Secant

Graphing Cosecant and Secant

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Graphing Cosecant and Secant

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  1. Graphing Cosecant and Secant

  2. 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

  3. Press Y= • y1 = sin (x) • y2 = 1/sin (x) Press Graph

  4. Press Y= • y1 = 3sin (X) • y2 = 3/sin(x) Press Graph

  5. Press Y= • y1 = sin (X) + 1 • y2 = 1/sin (X) +1 Press Graph

  6. Press Y= • y1 = sin (x + 1) • y2 = 1/sin (x +1) Press Graph

  7. Press Y= • y1 = sin (2x) • y2 = 1/sin (2x) Press Graph

  8. 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.

  9. What do you think the secant curve will look like? • Check out your thoughts by … Press Y= • y1 = cos (x) • y2 = 1/cos (x)

  10. So, let’s graph cosecant and secant graphs.

  11. 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)

  12. 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)

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

  14. Graphing by Key Points • y = 2 csc x Think: ____________________ Amp = _________ Horizontal Shift = _______ Period = _______ Vertical Shift = _________ Inc. = ______ (0, ) (/2, ) (, ) (3/2, ) (2, )

  15. Graphing by Key Points • y = -2 sec x Think: ____________________ Amp = _________ Horizontal Shift = _______ Period = _______ Vertical Shift = _________ Inc. = ______ (0, ) (/2, ) (, ) (3/2, ) (2, )

  16. Graphing by Key Points • y = sec 4x Think: ____________________ Amp = _________ Horizontal Shift = _______ Period = _______ Vertical Shift = _________ Inc. = ______ (0, ) (/8, ) (/4, ) (3/8, ) (/2, )

  17. Graphing by Key Points • y = 3 csc 1/2x Think: ____________________ Amp = _________ Horizontal Shift = _______ Period = _______ Vertical Shift = _________ Inc. = _____ (0, ) (, ) (2, ) (3, ) (4, )

  18. Graphing by Key Points • y = 3 sec x +2 Think: ____________________ Amp = _________ Horizontal Shift = _______ Period = _______ Vertical Shift = _________ Inc. = ______ (0, ) (/2 ) (, ) (3/2, ) (2, )

  19. Graphing by Key Points • y = sec x +2 Think: ____________________ Amp = _________ Horizontal Shift = _______ Period = _______ Vertical Shift = _________ Inc. = ______ (0, ) (/2 ) (, ) (3/2, ) (2, )

  20. Graphing by Key Points • y = csc (x + ) Think: ____________________ Amp = _________ Horizontal Shift = _______ Period = _______ Vertical Shift = _________ Inc. = ______ (-, ) (-/2 ) (0, ) (/2, ) (, )

  21. 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, )

  22. Graphing by Key Points • y = 2 sec (x/2 - /2) -1 Think: ________________ Amp = _________ Horizontal Shift = _______ Period = _______ Vertical Shift = _________ Inc. = ______ (, ) (2, ) (3, ) (4, ) (5, )