1. Graphing Trigonometric Functions Chapter 4

2. The sine and cosine curves Graph y = sinx

3. The sine and cosine curves Graph y = cosx

4. The sine and cosine curves Graph y = -cosx

5. The sine and cosine curves Graph y = -sinx

6. Amplitude “a” y = asinxy = acosx The amplitude will stretch the graph vertically. The value of “a” is half the distance of the max and min.

7. Amplitude “a” Graph y = 3cosx

8. Period of the sine and cosine y = sinbx and y = cosbx The period of the function will shrink or stretch the graph horizontally. The period of a function is The standard period is 2π, this occurs when b = 1.

9. Period of the sine and cosine Graph y = sin3x

10. Period of the sine and cosine Graph y = cos2x

11. Amplitude “a” and Period ”b” Graph y = 3sin4x

12. Amplitude “a” and Period ”b” Graph y = -4cosπx

13. Phase Shifts of sine and cosine y = sinb(x-d) and y = cosb(x-d) The period of the function will have new endpoints when solving the inequality 0 ≤ b(x-d) ≤ 2π. (x – d) is a shift of “d” to the right (x + d) is a shift of “d” to the left

14. Phase Shifts of sine and cosine Graph

15. Phase Shifts of sine and cosine Graph

16. Vertical Translations of sine and cosine y = c + sinx and y = c + cosx The “c” will shift the entire graph “c” units up when “c” is positive and “c” units down when “c” is negative

17. Vertical Translations of sine and cosine Graph y = 2 + sinx

18. Vertical Translations of sine and cosine Graph y = -2 + cos3x

19. Graph y = -2 – 2sin5x Combinations of Translations

20. Graph y = 1 -2cos3(x+π) Combinations of Translations

21. Graph

22. Identifying Features Give the amplitude, period, phase shift, and vertical translation. Amplitude: 2 Period: 2π Phase Shift: π/3 to the left Vertical Translation: none

23. Identifying Features Give the amplitude, period, phase shift, and vertical translation. Amplitude: 1 Period: 2π/3 Phase Shift: π/6 to the right Vertical Translation: up 1

24. Identifying Features Give the amplitude, period, phase shift, and vertical translation. Amplitude: 4 Period: π Phase Shift: π to the right Vertical Translation: down 2

25. Graph y = secx Graphs of Secant and Cosecant

26. Graph y = cscx Graphs of Secant and Cosecant

27. Graph y = 2csc5x Graphs of Secant and Cosecant

28. Find the amplitude, period, phase shift, and vertical translation…then graph it. Amplitude: not applicable Period: π Phase Shift: π/6 to the left Vertical Translation: down 1

29. Graphs of Secant and Cosecant Find the amplitude, period, phase shift, and vertical translation…then graph it.

30. Graphs of Secant and Cosecant Find the amplitude, period, phase shift, and vertical translation…then graph it. Amplitude: not applicable Period: 2π Phase Shift: π/4 to the right Vertical Translation: up 2

31. Graphs of Secant and Cosecant Find the amplitude, period, phase shift, and vertical translation…then graph it.

32. Over “2-periods” Graph y = sinx

33. Over “2-periods” Graph

34. Tangent and Cotangent Sine,Cosine,Secant, and Cosecant have a standard period of 2π. The tangent and cotangent have a standard period of π. The standard tangent graph has asymptotes at –π/2 and π/2 The standard cotangent graph has asymptotes at 0 and π

35. Tangent and Cotangent Graph y = tanx

36. Tangent and Cotangent Graph y = cotx

37. Tangent and Cotangent Graph y = 1 – tan3x

38. Tangent and Cotangent Graph y = 2 + 3cot(x – π) Amplitude: not applicable Period: π Phase Shift: π to the right Vertical Translation: up 2 Find the amplitude, period, phase shift, and vertical translation…then graph it.

39. Tangent and Cotangent Graph y = 2 + 3cot(x – π) Find the amplitude, period, phase shift, and vertical translation…then graph it.

40. Graph y = 1 + tan(2x + π) Graph the following over 2 periods

41. Tangent and Cotangent Graph Period: π/2 Phase Shift: π/8 to the left Vertical Translation: up 1 Find the amplitude, period, phase shift, and vertical translation…then graph it. Amplitude: not applicable

42. Tangent and Cotangent Graph Find the amplitude, period, phase shift, and vertical translation…then graph it.

43. A chart for you

44. Write the equation of a graph given the following information. 1. A negative Cosine function, amplitude 2, period π, phase shift π/2 to the left, vertical translation down 2. 2. A positive Sine function, amplitude 1, period π/4, phase shift π to the right, vertical translation up 1. 3. A negative Tangent function, period π, phase shift π to the left, vertical translation down 1. Y = -2-2cos(2x + π) Y = 1 + sin(8x – 8π) Y = -1-tan(x + π)

45. Write the equation of a graph. Y = 2cos2x

46. Write the equation of a graph. or

47. Write the equation of a graph.

48. TEAMS p. 181…….#’s 17-22

49. Write an equation for one cycle of this tide graph. November 3 rd 2014

50. Write the equation for this graph: Y=secx

51. Write the equation for this graph: Y=1+2cos2x

52. Write the equation for this graph:

57. Ch4 HW #7