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Graphing Tangent and Cotangent

Graphing Tangent and Cotangent. Graphing Tangent 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 = tan (x). Graphing Cotangent 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 = cot (x).

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Graphing Tangent and Cotangent

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  1. Graphing Tangent and Cotangent

  2. Graphing Tangent 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 = tan (x)

  3. Graphing Cotangent 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 = cot (x)

  4. Using the Graphing Calculator • Mode— • Radians • Function • Sequential • Window— • X min = -  • X max = 3 • X scale = /6 • Window— • Y min =-3 • Y max = 3 • Y scale = .5

  5. Press Y= • y1 = tan (x) • y2 = 3tan (x) Press Graph

  6. Press Y= • y1 = tan (x) • y2 = 4tan (x) Press Graph

  7. Press Y= • y1 = tan (x) • y2 = -4tan (x) Press Graph

  8. Press Y= • y1 = tan (x) • y2 = tan (x) +1 Press Graph

  9. Press Y= • y1 = tan (x) • y2 = tan (x +1) Press Graph

  10. Press Y= • y1 = tan (x) • y2 = tan (2x) Press Graph

  11. Press Y= • y1 = tan (x) • y2 = tan (1/2x) Press Graph

  12. Vertical Shift up/down Y = A tan (Bx - C) ± D Period  |B| No Amplitude, but determines two points on the graph. Horizontal Shift Left/Right C B

  13. y = A tan (Bx – C) + D Intercept Maximum? Asymptote Minimum? Intercept Unless A = Negative # Intercept Minimum? Asymptotes Maximum? Intercept

  14. y = cot (x) Press Y= • y1 = 1/tan (x) • y2 = 3/tan (x) Press Graph

  15. Press Y= • y1 = 1/tan (x) • y2 = 4/tan (x) Press Graph

  16. Press Y= • y1 = 1/tan (x) • y2 = -4/tan (x) Press Graph

  17. Press Y= • y1 = 1/tan (x) • y2 = 1/tan (x) +1 Press Graph

  18. Press Y= • y1 = 1/tan (x) • y2 = 1/tan (x +1) Press Graph

  19. Press Y= • y1 = 1/tan (x) • y2 = 1/tan (2x) Press Graph

  20. Vertical Shift up/down Y = A cot (Bx - C) ± D Period  |B| No Amplitude, but determines two points on the graph. Horizontal Shift Left/Right C B

  21. y = A cot (Bx – C) + D Asymptote Maximum? Intercept Minimum? Asymptote Unless A = Negative # Asymptote Minimum? Intercept Maximum? Asymptote

  22. Examples-- • y = 3tan (x + 1) -3 Amp.= _______ Period = _____ Horizontal Phase Shift = _________ Vertical Phase Shift = ________ • y = cot (x - 2) Amp.= _______ Period = _____ Horizontal Phase Shift = _________ Vertical Phase Shift = ________

  23. y = cot (2x) Amp.= _______ Period = _____ Horizontal Phase Shift = _________ Vertical Phase Shift = ________ y = ½ tan (½ x) + 1 Amp.= _______ Period = _____ Horizontal Phase Shift = _________ Vertical Phase Shift = ________

  24. Graphing by Key Points • y = 2 tan x Amp = _________ Horizontal Shift = _______ Period = _______ Vertical Shift = _________ Inc. = ________ (0, ) (/4, ) (/2, ) (3/4, ) (, )

  25. Graphing by Key Points • y = -2 cot x Amp = _________ Horizontal Shift = _______ Period = _______ Vertical Shift = _________ Inc. = ________ (0, ) (/4, ) (/2, ) (3/4, ) (, )

  26. Graphing by Key Points • y = tan (1/2x) Amp = _________ Horizontal Shift = _______ Period = _______ Vertical Shift = _________ Inc. = ________ (0, ) (/2, ) ( , ) (3/2, ) (2, )

  27. Graphing by Key Points • y = 3 cot 1/2x Amp = _________ Horizontal Shift = _______ Period = _______ Vertical Shift = _________ Inc. = ________ (0, ) (/2, ) (, ) (3/2, ) (2, )

  28. Graphing by Key Points • y = 3 tan x +2 Amp = _________ Horizontal Shift = _______ Period = _______ Vertical Shift = _________ Inc. = ________ (0, ) (/4 ) (/2, ) (3/4, ) (, )

  29. Graphing by Key Points • y = cot x - 2 Amp = _________ Horizontal Shift = _______ Period = _______ Vertical Shift = _________ Inc. = ________ (0, ) (/4 ) (/2, ) (3/2, ) (, )

  30. Graphing by Key Points • y = -tan (x + ) Amp = _________ Horizontal Shift = _______ Period = _______ Vertical Shift = _________ Inc. = ________ (-, ) (-3/4 , ) (-/2 , ) (-/4, ) (0, )

  31. Graphing by Key Points • y = cot (x - /4) Amp = _________ Horizontal Shift = _______ Period = _______ Vertical Shift = _________ Inc. = ________ (/4 , ) (/2, ) (3/4, ) (, ) (5/4, )

  32. Graphing by Key Points • y = 4tan (x/2 + /2) Amp = _________ Horizontal Shift = _______ Period = _______ Vertical Shift = _________ Inc. = ________ (-, ) (-/2 , ) (0, ) (/2, ) (, )

  33. Graphing by Key Points • y = -cot x Amp = _________ Horizontal Shift = _______ Period = _______ Vertical Shift = _________ Inc. = ________ (0, ) (1/4, ) (1/2, ) (3/4, ) (1, )

  34. Graphing by Key Points • y = 2tan (x/2 - /2) -1 Amp = _________ Horizontal Shift = _______ Period = _______ Vertical Shift = _________ Inc. = ________ (, ) (3/2, ) (2, ) (5/2, ) (3, )

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