1. Graphing Tangent and Cotangent

2. Graphing Tangent Curve y = tan (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 

3. Graphing Cotangent Curve y = cot (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 

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= y 1 = tan (x) y 2 = 3tan (x) Press Graph

6. Press Y= y 1 = tan (x) y 2 = 4tan (x) Press Graph

7. Press Y= y 1 = tan (x) y 2 = -4tan (x) Press Graph

8. Press Y= y 1 = tan (x) y 2 = tan (x) +1 Press Graph

9. Press Y= y 1 = tan (x) y 2 = tan (x +1) Press Graph

10. Press Y= y 1 = tan (x) y 2 = tan (2x) Press Graph

11. Press Y= y 1 = tan (x) y 2 = tan (1/2x) Press Graph

12. Y = A tan (Bx - C) ± D No Amplitude, but determines two points on the graph. Period  |B| Vertical Shift up/down 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. Press Y= y 1 = 1/tan (x) y 2 = 3/tan (x) Press Graph y = cot (x)

15. Press Y= y 1 = 1/tan (x) y 2 = 4/tan (x) Press Graph

16. Press Y= y 1 = 1/tan (x) y 2 = -4/tan (x) Press Graph

17. Press Y= y 1 = 1/tan (x) y 2 = 1/tan (x) +1 Press Graph

18. Press Y= y 1 = 1/tan (x) y 2 = 1/tan (x +1) Press Graph

19. Press Y= y 1 = 1/tan (x) y 2 = 1/tan (2x) Press Graph

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

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 / 2 x 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 , )