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12 x1 t03 02 graphing trig functions (2012)

N
Nigel Simmons

The document discusses graphing trigonometric functions like sine and cosine curves. It explains that a sine curve is defined by the equation y = a sin(bx + c), where the period is 2π/b units, the amplitude is a units, and c shifts the curve left or right. A worked example with the equation y = 5 sin(9x - π/2) is shown. The cosine curve is similarly defined by y = a cos(bx + c), with the same period, amplitude, and shift properties. An example equation of y = -4 cos((x + π)/8) + 2 is provided and its graphing details are described.

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Graphing Trig Functions
Graphing Trig 1) Sine Curve Functions
Graphing Trig 1) Sine Curve Functions y 1 -1
Graphing Trig 1) Sine Curve Functions y 1  2   2 3 4 x -1
Graphing Trig 1) Sine Curve Functions y 1  2   2 3 4 x -1
Graphing Trig 1) Sine Curve Functions y 1  2   2 3 4 x -1
Graphing Trig 1) Sine Curve Functions y 1  2   2 3 4 x -1
Graphing Trig 1) Sine Curve Functions y 1 y  sin x  2   2 3 4 x -1
Graphing Trig 1) Sine Curve Functions y 1 y  sin x  2   2 3 4 x -1 domain : all real x
Graphing Trig 1) Sine Curve Functionsy 1 y  sin x  2   2 3 4 x -1 domain : all real x range : - 1  y  1
Graphing Trig 1) Sine Curve Functionsy period 1 y  sin x  2   2 3 4 x -1 domain : all real x range : - 1  y  1
Graphing Trig 1) Sine Curve Functionsy period 1 y  sin x  2   2 3 4 x -1 In general; domain : all real x y  a sin bx  c  range : - 1  y  1 2 period  units b
Graphing Trig 1) Sine Curve Functions y period 1 y  sin x amplitude  2   2 3 4 x -1 In general; domain : all real x y  a sin bx  c  range : - 1  y  1 2 period  units b
Graphing Trig 1) Sine Curve Functions y period 1 y  sin x amplitude  2   2 3 4 x -1 In general; domain : all real x y  a sin bx  c  range : - 1  y  1 2 period  units b amplitude  a units
Graphing Trig 1) Sine Curve Functions y period 1 y  sin x amplitude  2   2 3 4 x -1 In general; domain : all real x y  a sin bx  c  range : - 1  y  1 2 period period  units divisions  b 4 amplitude  a units
Graphing Trig 1) Sine Curve Functions y period 1 y  sin x amplitude  2   2 3 4 x -1 In general; domain : all real x y  a sin bx  c  range : - 1  y  1 2 period period  units divisions  b 4 c amplitude  a units shift  to left b
 e.g. y  5 sin  9 x      2
 e.g. y  5 sin  9 x     2  2 period  units 9
 e.g. y  5 sin  9 x     2  2 period  units 9 amplitude  5 units
 e.g. y  5 sin  9 x     2   2 period  units divisions  9 18 amplitude  5 units
 e.g. y  5 sin  9 x     2   2 period  units divisions  9 18  amplitude  5 units shift  to right 18
 e.g. y  5 sin  9 x     2   2 period  units divisions  9 18  amplitude  5 units shift  to right 18 y 5   2  x 9 -5 9 9
 e.g. y  5 sin  9 x     2   2 period  units divisions  9 18  amplitude  5 units shift  to right 18 y 5   2  x 9 -5 9 9
 e.g. y  5 sin  9 x     2   2 period  units divisions  9 18  amplitude  5 units shift  to right 18 y 5   2  x 9 -5 9 9
 e.g. y  5 sin  9 x     2   2 period  units divisions  9 18  amplitude  5 units shift  to right 18 y 5   2  x 9 -5 9 9
 e.g. y  5 sin  9 x     2   2 period  units divisions  9 18  amplitude  5 units shift  to right 18 y 5   2  x 9 -5 9 9
 e.g. y  5 sin  9 x     2   2 period  units divisions  9 18  amplitude  5 units shift  to right 18 y  9x    y  5 sin   5  2    2  x 9 -5 9 9
2) Cosine Curve
2) Cosine Curve y  a cosbx  c 
2) Cosine Curve y  a cosbx  c  2 period  units b
2) Cosine Curve y  a cosbx  c  2 period  units b amplitude  a units
2) Cosine Curve y  a cosbx  c  2 period period  units divisions  b 4 amplitude  a units
2) Cosine Curve y  a cosbx  c  2 period period  units divisions  b 4 c amplitude  a units shift  to left b
2) Cosine Curve y  a cosbx  c  2 period period  units divisions  b 4 c amplitude  a units shift  to left b  x    2 e.g. y  4 cos   8 
2) Cosine Curve y  a cosbx  c  2 period period  units divisions  b 4 c amplitude  a units shift  to left b  x    2 2 e.g. y  4 cos  period  8  1 8  16
2) Cosine Curve y  a cosbx  c  2 period period  units divisions  b 4 c amplitude  a units shift  to left b  x    2 2 e.g. y  4 cos  period  8  1 8  16 amplitude  4
2) Cosine Curve y  a cosbx  c  2 period period  units divisions  b 4 c amplitude  a units shift  to left b  x    2 2 e.g. y  4 cos  period  divisions  4 8  1 8  16 amplitude  4
2) Cosine Curve y  a cosbx  c  2 period period  units divisions  b 4 c amplitude  a units shift  to left b  x    2 2 e.g. y  4 cos  period  divisions  4 8  1 8 shift  8 to left, 2 up,  16 upside down amplitude  4
2) Cosine Curve y  a cosbx  c  2 period period  units divisions  b 4 c amplitude  a units shift  to left b  x    2 2 e.g. y  4 cos  period  divisions  4 8  1 8 shift  8 to left, 2 up,  16 upside down y amplitude  4 6 2  8 8 16 x -2
2) Cosine Curve y  a cosbx  c  2 period period  units divisions  b 4 c amplitude  a units shift  to left b  x    2 2 e.g. y  4 cos  period  divisions  4 8  1 8 shift  8 to left, 2 up,  16 upside down y amplitude  4 6 2  8 8 16 x -2
2) Cosine Curve y  a cosbx  c  2 period period  units divisions  b 4 c amplitude  a units shift  to left b  x    2 2 e.g. y  4 cos  period  divisions  4 8  1 8 shift  8 to left, 2 up,  16 upside down y amplitude  4 6 2  8 8 16 x -2
2) Cosine Curve y  a cosbx  c  2 period period  units divisions  b 4 c amplitude  a units shift  to left b  x    2 2 e.g. y  4 cos  period  divisions  4 8  1 8 shift  8 to left, 2 up,  16 upside down y amplitude  4 6 2  8 8 16 x -2
2) Cosine Curve y  a cosbx  c  2 period period  units divisions  b 4 c amplitude  a units shift  to left b  x    2 2 e.g. y  4 cos  period  divisions  4 8  1 8 shift  8 to left, 2 up,  16 upside down y amplitude  4 6 2  8 8 16 x -2
2) Cosine Curve y  a cosbx  c  2 period period  units divisions  b 4 c amplitude  a units shift  to left b  x    2 2 e.g. y  4 cos  period  divisions  4 8  1 8 shift  8 to left, 2 up,  16 upside down y amplitude  4 y  4 cos     2  x 6  8  2  8 8 16 x -2
3) Tangent Curve
3) Tangent Curve y  a tan bx  c 
3) Tangent Curve y  a tan bx  c   period  units b
3) Tangent Curve y  a tan bx  c  divisions  period  2 period  units b
3) Tangent Curve y  a tan bx  c  divisions  period  c 2 period  units shift  to left b b
3) Tangent Curve y  a tan bx  c  divisions  period  c 2 period  units shift  to left b b e.g. y  e tan x  2 
3) Tangent Curve y  a tan bx  c  divisions  period  c 2 period  units shift  to left b b e.g. y  e tan x  2   period   1
3) Tangent Curve y  a tan bx  c  divisions  period  c 2 period  units shift  to left b b e.g. y  e tan x  2   1 period  divisions   2 1
3) Tangent Curve y  a tan bx  c  divisions  period  c 2 period  units shift  to left b b e.g. y  e tan x  2   1 period  divisions   2 1 shift  2 to right
3) Tangent Curve y  a tan bx  c  divisions  period  c 2 period  units shift  to left b b e.g. y  e tan x  2   1 period  divisions   2 1 shift  2 to right y 1 2 x
3) Tangent Curve y  a tan bx  c  divisions  period  c 2 period  units shift  to left b b e.g. y  e tan x  2   1 period  divisions   2 1 shift  2 to right y 1 2 x
3) Tangent Curve y  a tan bx  c  divisions  period  c 2 period  units shift  to left b b e.g. y  e tan x  2   1 period  divisions   2 1 shift  2 to right y 1 2 x
3) Tangent Curve y  a tan bx  c  divisions  period  c 2 period  units shift  to left b b e.g. y  e tan x  2   1 period  divisions   2 1 shift  2 to right y y  e tan x  2  1 2 x
3) Tangent Curve y  a tan bx  c  divisions  period  c 2 period  units shift  to left b b e.g. y  e tan x  2   1 period  divisions   2 1 shift  2 to right y y  e tan x  2  Exercise 14C; 2b, 3b, 1 2 x 4b, 5bce, 8, 9, 10b, 13, 15, 16, 17, 20

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12 x1 t03 02 graphing trig functions (2012)

  • 2. Graphing Trig 1) Sine Curve Functions
  • 3. Graphing Trig 1) Sine Curve Functions y 1 -1
  • 4. Graphing Trig 1) Sine Curve Functions y 1  2   2 3 4 x -1
  • 5. Graphing Trig 1) Sine Curve Functions y 1  2   2 3 4 x -1
  • 6. Graphing Trig 1) Sine Curve Functions y 1  2   2 3 4 x -1
  • 7. Graphing Trig 1) Sine Curve Functions y 1  2   2 3 4 x -1
  • 8. Graphing Trig 1) Sine Curve Functions y 1 y  sin x  2   2 3 4 x -1
  • 9. Graphing Trig 1) Sine Curve Functions y 1 y  sin x  2   2 3 4 x -1 domain : all real x
  • 10. Graphing Trig 1) Sine Curve Functionsy 1 y  sin x  2   2 3 4 x -1 domain : all real x range : - 1  y  1
  • 11. Graphing Trig 1) Sine Curve Functionsy period 1 y  sin x  2   2 3 4 x -1 domain : all real x range : - 1  y  1
  • 12. Graphing Trig 1) Sine Curve Functionsy period 1 y  sin x  2   2 3 4 x -1 In general; domain : all real x y  a sin bx  c  range : - 1  y  1 2 period  units b
  • 13. Graphing Trig 1) Sine Curve Functions y period 1 y  sin x amplitude  2   2 3 4 x -1 In general; domain : all real x y  a sin bx  c  range : - 1  y  1 2 period  units b
  • 14. Graphing Trig 1) Sine Curve Functions y period 1 y  sin x amplitude  2   2 3 4 x -1 In general; domain : all real x y  a sin bx  c  range : - 1  y  1 2 period  units b amplitude  a units
  • 15. Graphing Trig 1) Sine Curve Functions y period 1 y  sin x amplitude  2   2 3 4 x -1 In general; domain : all real x y  a sin bx  c  range : - 1  y  1 2 period period  units divisions  b 4 amplitude  a units
  • 16. Graphing Trig 1) Sine Curve Functions y period 1 y  sin x amplitude  2   2 3 4 x -1 In general; domain : all real x y  a sin bx  c  range : - 1  y  1 2 period period  units divisions  b 4 c amplitude  a units shift  to left b
  • 17.  e.g. y  5 sin  9 x      2
  • 18.  e.g. y  5 sin  9 x     2  2 period  units 9
  • 19.  e.g. y  5 sin  9 x     2  2 period  units 9 amplitude  5 units
  • 20.  e.g. y  5 sin  9 x     2   2 period  units divisions  9 18 amplitude  5 units
  • 21.  e.g. y  5 sin  9 x     2   2 period  units divisions  9 18  amplitude  5 units shift  to right 18
  • 22.  e.g. y  5 sin  9 x     2   2 period  units divisions  9 18  amplitude  5 units shift  to right 18 y 5   2  x 9 -5 9 9
  • 23.  e.g. y  5 sin  9 x     2   2 period  units divisions  9 18  amplitude  5 units shift  to right 18 y 5   2  x 9 -5 9 9
  • 24.  e.g. y  5 sin  9 x     2   2 period  units divisions  9 18  amplitude  5 units shift  to right 18 y 5   2  x 9 -5 9 9
  • 25.  e.g. y  5 sin  9 x     2   2 period  units divisions  9 18  amplitude  5 units shift  to right 18 y 5   2  x 9 -5 9 9
  • 26.  e.g. y  5 sin  9 x     2   2 period  units divisions  9 18  amplitude  5 units shift  to right 18 y 5   2  x 9 -5 9 9
  • 27.  e.g. y  5 sin  9 x     2   2 period  units divisions  9 18  amplitude  5 units shift  to right 18 y  9x    y  5 sin   5  2    2  x 9 -5 9 9
  • 29. 2) Cosine Curve y  a cosbx  c 
  • 30. 2) Cosine Curve y  a cosbx  c  2 period  units b
  • 31. 2) Cosine Curve y  a cosbx  c  2 period  units b amplitude  a units
  • 32. 2) Cosine Curve y  a cosbx  c  2 period period  units divisions  b 4 amplitude  a units
  • 33. 2) Cosine Curve y  a cosbx  c  2 period period  units divisions  b 4 c amplitude  a units shift  to left b
  • 34. 2) Cosine Curve y  a cosbx  c  2 period period  units divisions  b 4 c amplitude  a units shift  to left b  x    2 e.g. y  4 cos   8 
  • 35. 2) Cosine Curve y  a cosbx  c  2 period period  units divisions  b 4 c amplitude  a units shift  to left b  x    2 2 e.g. y  4 cos  period  8  1 8  16
  • 36. 2) Cosine Curve y  a cosbx  c  2 period period  units divisions  b 4 c amplitude  a units shift  to left b  x    2 2 e.g. y  4 cos  period  8  1 8  16 amplitude  4
  • 37. 2) Cosine Curve y  a cosbx  c  2 period period  units divisions  b 4 c amplitude  a units shift  to left b  x    2 2 e.g. y  4 cos  period  divisions  4 8  1 8  16 amplitude  4
  • 38. 2) Cosine Curve y  a cosbx  c  2 period period  units divisions  b 4 c amplitude  a units shift  to left b  x    2 2 e.g. y  4 cos  period  divisions  4 8  1 8 shift  8 to left, 2 up,  16 upside down amplitude  4
  • 39. 2) Cosine Curve y  a cosbx  c  2 period period  units divisions  b 4 c amplitude  a units shift  to left b  x    2 2 e.g. y  4 cos  period  divisions  4 8  1 8 shift  8 to left, 2 up,  16 upside down y amplitude  4 6 2  8 8 16 x -2
  • 40. 2) Cosine Curve y  a cosbx  c  2 period period  units divisions  b 4 c amplitude  a units shift  to left b  x    2 2 e.g. y  4 cos  period  divisions  4 8  1 8 shift  8 to left, 2 up,  16 upside down y amplitude  4 6 2  8 8 16 x -2
  • 41. 2) Cosine Curve y  a cosbx  c  2 period period  units divisions  b 4 c amplitude  a units shift  to left b  x    2 2 e.g. y  4 cos  period  divisions  4 8  1 8 shift  8 to left, 2 up,  16 upside down y amplitude  4 6 2  8 8 16 x -2
  • 42. 2) Cosine Curve y  a cosbx  c  2 period period  units divisions  b 4 c amplitude  a units shift  to left b  x    2 2 e.g. y  4 cos  period  divisions  4 8  1 8 shift  8 to left, 2 up,  16 upside down y amplitude  4 6 2  8 8 16 x -2
  • 43. 2) Cosine Curve y  a cosbx  c  2 period period  units divisions  b 4 c amplitude  a units shift  to left b  x    2 2 e.g. y  4 cos  period  divisions  4 8  1 8 shift  8 to left, 2 up,  16 upside down y amplitude  4 6 2  8 8 16 x -2
  • 44. 2) Cosine Curve y  a cosbx  c  2 period period  units divisions  b 4 c amplitude  a units shift  to left b  x    2 2 e.g. y  4 cos  period  divisions  4 8  1 8 shift  8 to left, 2 up,  16 upside down y amplitude  4 y  4 cos     2  x 6  8  2  8 8 16 x -2
  • 46. 3) Tangent Curve y  a tan bx  c 
  • 47. 3) Tangent Curve y  a tan bx  c   period  units b
  • 48. 3) Tangent Curve y  a tan bx  c  divisions  period  2 period  units b
  • 49. 3) Tangent Curve y  a tan bx  c  divisions  period  c 2 period  units shift  to left b b
  • 50. 3) Tangent Curve y  a tan bx  c  divisions  period  c 2 period  units shift  to left b b e.g. y  e tan x  2 
  • 51. 3) Tangent Curve y  a tan bx  c  divisions  period  c 2 period  units shift  to left b b e.g. y  e tan x  2   period   1
  • 52. 3) Tangent Curve y  a tan bx  c  divisions  period  c 2 period  units shift  to left b b e.g. y  e tan x  2   1 period  divisions   2 1
  • 53. 3) Tangent Curve y  a tan bx  c  divisions  period  c 2 period  units shift  to left b b e.g. y  e tan x  2   1 period  divisions   2 1 shift  2 to right
  • 54. 3) Tangent Curve y  a tan bx  c  divisions  period  c 2 period  units shift  to left b b e.g. y  e tan x  2   1 period  divisions   2 1 shift  2 to right y 1 2 x
  • 55. 3) Tangent Curve y  a tan bx  c  divisions  period  c 2 period  units shift  to left b b e.g. y  e tan x  2   1 period  divisions   2 1 shift  2 to right y 1 2 x
  • 56. 3) Tangent Curve y  a tan bx  c  divisions  period  c 2 period  units shift  to left b b e.g. y  e tan x  2   1 period  divisions   2 1 shift  2 to right y 1 2 x
  • 57. 3) Tangent Curve y  a tan bx  c  divisions  period  c 2 period  units shift  to left b b e.g. y  e tan x  2   1 period  divisions   2 1 shift  2 to right y y  e tan x  2  1 2 x
  • 58. 3) Tangent Curve y  a tan bx  c  divisions  period  c 2 period  units shift  to left b b e.g. y  e tan x  2   1 period  divisions   2 1 shift  2 to right y y  e tan x  2  Exercise 14C; 2b, 3b, 1 2 x 4b, 5bce, 8, 9, 10b, 13, 15, 16, 17, 20