From Event to Action: Accelerate Your Decision Making with Real-Time Automation
D.E.V part 1
1.
2. It’s been 3 years since the day Zack and Sally falling in love with each other.
3. Before that day, Zack, Sally’s boyfriend, has been thinking about this day long times before. He wants to give her a big surprise.
4. Before that day, Zack, Sally’s boyfriend, has been thinking about this day long times before. He wants to give her a big surprise.
5. Before that day, Zack, Sally’s boyfriend, has been thinking about this day long times before. He wants to give her a big surprise. What should I do to make her feel happy ?????
8. Romantic night at the 5 stars restaurant. He’s thinking of ... He’s thinking of ... He’s thinking of ...
9. Romantic night at the 5 stars restaurant. Or going shopping!!! He’s thinking of ...
10. Romantic night at the 5 stars restaurant. Or going shopping!!! Or a romantic movie He’s thinking of ...
11. Romantic night at the 5 stars restaurant. Or going shopping!!! Or a romantic movie Make their love symbols He’s thinking of ...
12. Romantic night at the 5 stars restaurant. Or going shopping!!! Or a romantic movie Make their love symbols Or walking together at night He’s thinking of ...
29. Solving: First we have to draw the graph so that we can easily solve this problem. m min
30. Solving: First we have to draw the graph so that we can easily solve this problem. Maximum height : 32m 32 m min
31. Solving: First we have to draw the graph so that we can easily solve this problem. Maximum height : 32m 32 Stain 2m above the ground 2 m min
32. Solving: First we have to draw the graph so that we can easily solve this problem. Maximum height : 32m 32 Stain 2m above the ground 2 m min Go from bottom to the top : 6mins half period = 6mins 6
33. Solving: First we have to draw the graph so that we can easily solve this problem. Maximum height : 32m 32 Stain 2m above the ground 2 m min Go from bottom to the top : 6mins half period = 6mins 6 = 15 [ the distance from the max and min points to the Sinusoidal Axis.] 17 (An Amplitude) (32-2) 2
34. Solving: First we have to draw the graph so that we can easily solve this problem. Maximum height : 32m 32 Stain 2m above the ground 2 m min Go from bottom to the top : 6mins half period = 6mins 6 = 15 [ the distance from the max and min points to the Sinusoidal Axis.] 17 15 15 (An Amplitude) (32-2) 2
35. Solving: First we have to draw the graph so that we can easily solve this problem. Maximum height : 32m 32 Stain 2m above the ground 2 m min Go from bottom to the top : 6mins half period = 6mins 6 = 15 [ the distance from the max and min points to the Sinusoidal Axis.] 17 From the information above, we can sketch the graph. (An Amplitude) (32-2) 2
36. Solving: First we have to draw the graph so that we can easily solve this problem. Maximum height : 32m 32 Stain 2m above the ground 2 m min Go from bottom to the top : 6mins half period = 6mins 6 = 15 [ the distance from the max and min points to the Sinusoidal Axis.] 17 From the information above, we can sketch the graph. Sinusoidal axis (An Amplitude) (32-2) 2
37. Solving: First we have to draw the graph so that we can easily solve this problem. Maximum height : 32m 32 Stain 2m above the ground 2 m min Go from bottom to the top : 6mins half period = 6mins 6 = 15 [ the distance from the max and min points to the Sinusoidal Axis.] 17 From the information above, we can sketch the graph. Sinusoidal axis P = 12mins 12 (An Amplitude) (32-2) 2
38. Solving: First we have to draw the graph so that we can easily solve this problem. Maximum height : 32m 32 Stain 2m above the ground 2 m min Go from bottom to the top : 6mins half period = 6mins 6 = 15 [ the distance from the max and min points to the Sinusoidal Axis.] 17 From the information above, we can sketch the graph. Sinusoidal axis P = 12mins 12 Max point (An Amplitude) (32-2) 2
39. Solving: First we have to draw the graph so that we can easily solve this problem. Maximum height : 32m 32 Stain 2m above the ground 2 m min Go from bottom to the top : 6mins half period = 6mins 6 = 15 [ the distance from the max and min points to the Sinusoidal Axis.] 17 From the information above, we can sketch the graph. Sinusoidal axis P = 12mins 12 Max point Min point (An Amplitude) (32-2) 2
40. Sine Function: f(x) = A sin B (x – C ) + D 32 2 m min 6 17 12
41. Sine Function: f(x) = A sin B (x – C ) + D A = B = C = D = 32 2 m min 6 17 12
42. Sine Function: f(x) = A sin B (x – C ) + D A = B = C = D = 15 32 2 m min 6 17 12
43. Sine Function: f(x) = A sin B (x – C ) + D 32 2 m min 6 17 12 15 A = B = C = D = 2 π P = 2 π 12 = π 6
44. Sine Function: f(x) = A sin B (x – C ) + D A = B = C = D = 15 3 [the graph shifts to the right] = = 32 2 m min 6 17 12 2 π P 2 π 12 π 6
45. Sine Function: f(x) = A sin B (x – C ) + D A = B = C = D = 15 = = 3 [the graph shifts to the right] +17 32 2 m min 6 17 12 2 π P 2 π 12 π 6
46. Sine Function: f(x) = A sin B (x – C ) + D A = B = C = D = 15 = = +17 f(x) = A sin B (x – C ) + D A = B = C = D = = = 15 A = B = C = D = = = 3 [the graph shifts to the right] 32 2 m min 6 17 12 2 π P 2 π 12 π 6 2 π P 2 π 12 π 6 2 π P 2 π 12 π 6
47. Sine Function: f(x) = A sin B (x – C ) + D f(x) = A sin B (x – C ) + D 32 2 m min 6 17 12 15 A = B = C = D = 2 π P = 2 π 12 = π 6 3 [the graph shifts to the right] +17 π 6 15 sin +17 (x – 3 )
48. Sine Function: f(x) = A sin B (x – C ) + D f(x) = A sin B (x – C ) + D Sub the value f(x) = 28m we get: 3 [the graph shifts to the right] 32 2 m min 6 17 12 15 A = B = C = D = 2 π P = 2 π 12 = π 6 +17 π 6 15 sin +17 (x – 3 )
49. Sine Function: f(x) = A sin B (x – C ) + D f(x) = A sin B (x – C ) + D Sub the value f(x) = 28m we get: 28 = 32 2 m min 6 17 12 3 [the graph shifts to the right] A = B = C = D = 15 2 π P = 2 π 12 = π 6 +17 π 6 15 sin +17 (x – 3 ) π 6 15 sin +17 (x – 3 )
65. If sinx = Cosy = Find cos2x + Sin2y From sinx, we could find cosx 7 12 1 2
66. If sinx = Cosy = Find cos2x + Sin2y From sinx, we could find cosx = 1 7 12 1 2 Sin x 2 + Cos x 2
67. If sinx = Cosy = Find cos2x + Sin2y From sinx, we could find cosx Sin x 2 + Cos x 2 - = 1 = 1 = 1 = 1 1 2 Cos x 2 Sin x 2 Sin x 2 Cos x 2 7 12
68. If sinx = Cosy = Find cos2x + Sin2y From sinx, we could find cosx Sin x 2 + Cos x 2 = 1 - = 1 = 1 = 1 - 2 = 1 1 2 Cos x 2 Sin x 2 Sin x 2 Cos x 2 Cos x 2 7 12 7 12 ( (
69. If sinx = Cosy = Find cos2x + Sin2y From sinx, we could find cosx Sin x 2 + Cos x 2 = 1 - = 1 = 1 = 1 - 2 = 1 - = 1 1 2 Cos x 2 Sin x 2 Sin x 2 Cos x 2 Cos x 2 7 12 7 12 ( ( Cos x 2 49 144
70. If sinx = Cosy = Find cos2x + Sin2y From sinx, we could find cosx Sin x 2 + Cos x 2 = 1 - = 1 = 1 = 1 - 2 = 1 - = = 1 1 2 Cos x 2 Sin x 2 Sin x 2 Cos x 2 Cos x 2 7 12 7 12 ( ( Cos x 2 49 144 Cos x 2 95 144
71. If sinx = Cosy = Find cos2x + Sin2y From sinx, we could find cosx Sin x 2 + Cos x 2 = 1 - = 1 = 1 = 1 - 2 = 1 - = Cosx = = 1 1 2 Cos x 2 Sin x 2 Sin x 2 Cos x 2 Cos x 2 7 12 7 12 ( ( Cos x 2 49 144 Cos x 2 95 144 √ 95 144
72. If sinx = Cosy = Find cos2x + Sin2y From sinx, we could find cosx Sin x 2 + Cos x 2 = 1 - = 1 = 1 = 1 - 2 = 1 - = Cosx = = 1 With the same method, we could find siny 1 2 Cos x 2 Sin x 2 Sin x 2 Cos x 2 Cos x 2 7 12 7 12 ( ( Cos x 2 49 144 Cos x 2 95 144 √ 95 144
73. If sinx = Cosy = Find cos2x + Sin2y From sinx, we could find cosx Sin x 2 + Cos x 2 = 1 - = 1 = 1 = 1 - 2 = 1 - = Cosx = = 1 With the same method, we could find siny Sin y 2 + 2 2 Cos y = 1 1 2 Cos x 2 Sin x 2 Sin x 2 Cos x 2 Cos x 2 7 12 7 12 ( ( Cos x 2 49 144 Cos x 2 95 144 √ 95 144 Sin y 2 2 2 Cos y
74. If sinx = Cosy = Find cos2x + Sin2y From sinx, we could find cosx Sin x 2 + Cos x 2 = 1 - = 1 = 1 = 1 - 2 = 1 - = Cosx = = 1 With the same method, we could find siny Sin y 2 + 2 2 Cos y = 1 = 1 - 1 2 Cos x 2 Sin x 2 Sin x 2 Cos x 2 Cos x 2 7 12 7 12 ( ( Cos x 2 49 144 Cos x 2 95 144 √ 95 144 Sin y 2 2 Sin y 2 2 2 Cos y 2 Cos y
75. If sinx = Cosy = Find cos2x + Sin2y From sinx, we could find cosx Sin x 2 + Cos x 2 = 1 - = 1 = 1 = 1 - 2 = 1 - = Cosx = = 1 With the same method, we could find siny Sin y 2 + 2 2 Cos y = 1 = 1 - = 1 - 1 2 Cos x 2 Sin x 2 Sin x 2 Cos x 2 Cos x 2 7 12 7 12 ( ( Cos x 2 49 144 Cos x 2 95 144 √ 95 144 Sin y 2 2 Sin y 2 2 2 Cos y 2 Cos y Sin y 2 2 1 2 ( ( 2
76. If sinx = Cosy = Find cos2x + Sin2y From sinx, we could find cosx Sin x 2 + Cos x 2 = 1 - = 1 = 1 = 1 - 2 = 1 - = Cosx = = 1 With the same method, we could find siny Sin y 2 + 2 2 Cos y = 1 = 1 - = 1 - = 1 - 1 2 Cos x 2 Sin x 2 Sin x 2 Cos x 2 Cos x 2 7 12 7 12 ( ( Cos x 2 49 144 Cos x 2 95 144 √ 95 144 Sin y 2 2 Sin y 2 2 2 Cos y 2 Cos y Sin y 2 2 1 2 ( ( 2 Sin y 2 2 1 4
77. If sinx = Cosy = Find cos2x + Sin2y From sinx, we could find cosx Sin x 2 + Cos x 2 = 1 - = 1 = 1 = 1 - 2 = 1 - = Cosx = = 1 With the same method, we could find siny Sin y 2 + 2 2 Cos y = 1 = 1 - = 1 - = 1 - = 1 2 Cos x 2 Sin x 2 Sin x 2 Cos x 2 Cos x 2 7 12 7 12 ( ( Cos x 2 49 144 Cos x 2 95 144 √ 95 144 Sin y 2 2 Sin y 2 2 2 Cos y 2 Cos y Sin y 2 2 1 2 ( ( 2 Sin y 2 2 1 4 Sin y 2 2 3 4
78. If sinx = Cosy = Find cos2x + Sin2y From sinx, we could find cosx Sin x 2 + Cos x 2 = 1 - = 1 = 1 = 1 - 2 = 1 - = Cosx = = 1 With the same method, we could find siny Sin y 2 + 2 2 Cos y = 1 = 1 - = 1 - = 1 - = Siny = 1 2 Cos x 2 Sin x 2 Sin x 2 Cos x 2 Cos x 2 7 12 7 12 ( ( Cos x 2 49 144 Cos x 2 95 144 √ 95 144 Sin y 2 2 Sin y 2 2 2 Cos y 2 Cos y Sin y 2 2 1 2 ( ( 2 Sin y 2 2 1 4 Sin y 2 2 3 4 √ 3 2 49 144
96. cos2x 1 + tanx cotx 1 sin2x 2 - 1 = + sin x 2 - ● cos2x 1 + tanx cos2x 1 + tanx cos2x = = - 1 + = - 1 + tanx cos2x 1 + tanx cos2x cos x 2 sin x 2 1 + tanx cos2x 1 + tanx cos2x sinx cosx sin x 2 cos x 2 sin x 2 cosx cosx + sinx
97. cos2x 1 + tanx cotx 1 sin2x 2 - 1 = + sin x 2 - ● cos2x 1 + tanx cos2x 1 + tanx cos2x = = - 1 + = - = - 1 x cosx cosx + sinx 1 + tanx cos2x 1 + tanx cos2x cos x 2 sin x 2 1 + tanx cos2x 1 + tanx cos2x sinx cosx sin x 2 cos x 2 sin x 2 cosx cosx + sinx sin x 2 cos x 2 sin x 2 - cos x 2 sin x 2 -
98. cos2x 1 + tanx cotx 1 sin2x 2 - 1 = + sin x 2 - ● cos2x 1 + tanx cos2x 1 + tanx cos2x = = - 1 + = - = - 1 x cosx cosx + sinx = cosx ( ) cosx + sinx 1 + tanx cos2x 1 + tanx cos2x cos x 2 sin x 2 1 + tanx cos2x 1 + tanx cos2x sinx cosx sin x 2 cos x 2 sin x 2 cosx cosx + sinx sin x 2 cos x 2 sin x 2 - cos x 2 sin x 2 - cos x 2 sin x 2 -
99. cos2x 1 + tanx cotx 1 sin2x 2 - 1 = + sin x 2 - ● cos2x 1 + tanx cos2x 1 + tanx cos2x = = - 1 + = - = - 1 x cosx cosx + sinx = cosx ( ) cosx + sinx = cosx (cosx + sinx) (cosx – sinx) cosx + sinx 1 + tanx cos2x 1 + tanx cos2x cos x 2 sin x 2 1 + tanx cos2x 1 + tanx cos2x sinx cosx sin x 2 cos x 2 sin x 2 cosx cosx + sinx sin x 2 cos x 2 sin x 2 - cos x 2 sin x 2 - cos x 2 sin x 2 -
100. cos2x 1 + tanx cotx 1 sin2x 2 - 1 = + sin x 2 - ● cos2x 1 + tanx cos2x 1 + tanx cos2x = = - 1 + = - = - 1 x cosx cosx + sinx = cosx ( ) cosx + sinx = cosx (cosx + sinx) (cosx – sinx) cosx + sinx 1 + tanx cos2x 1 + tanx cos2x cos x 2 sin x 2 1 + tanx cos2x 1 + tanx cos2x sinx cosx sin x 2 cos x 2 sin x 2 cosx cosx + sinx sin x 2 cos x 2 sin x 2 - cos x 2 sin x 2 - cos x 2 sin x 2 -
101. cos2x 1 + tanx cotx 1 sin2x 2 - 1 = + sin x 2 - ● cos2x 1 + tanx cos2x 1 + tanx cos2x = = - 1 + = - = - - 1 x cosx cosx + sinx = cosx ( ) cosx + sinx = cosx (cosx + sinx) (cosx – sinx) cosx + sinx 1 + tanx cos2x 1 + tanx cos2x cos x 2 sin x 2 1 + tanx cos2x 1 + tanx cos2x sinx cosx sin x 2 cos x 2 sin x 2 cosx cosx + sinx sin x 2 cos x 2 sin x 2 - cos x 2 sin x 2 cos x 2 sin x 2 - = cosx (cosx – sinx) ● cotx = cosx sinx
102. cos2x 1 + tanx cotx 1 sin2x 2 - 1 = + sin x 2 - ● cos2x 1 + tanx cos2x 1 + tanx cos2x = = - 1 + = - = - - 1 x cosx cosx + sinx = cosx ( ) cosx + sinx = cosx (cosx + sinx) (cosx – sinx) cosx + sinx = cosx (cosx – sinx) 1 + tanx cos2x 1 + tanx cos2x cos x 2 sin x 2 1 + tanx cos2x 1 + tanx cos2x sinx cosx sin x 2 cos x 2 sin x 2 cosx cosx + sinx sin x 2 cos x 2 sin x 2 - cos x 2 sin x 2 cos x 2 sin x 2 -
103. cos2x 1 + tanx cotx - 1 = cos2x 1 + tanx cos2x 1 + tanx cos2x = - 1 1 + tanx cos2x 1 sin2x 2 + sin x 2 - sin x 2 cosx sinx 1 sin2x 2 + sin x 2 - sin x 2 = cosx (cosx – sinx)
104. cos2x 1 + tanx cotx - 1 = cos2x 1 + tanx cos2x 1 + tanx cos2x = = - sinxcosx sinxcosx + sin x 2 - - sinxcosx 1 + tanx cos2x 1 sin2x 2 + sin x 2 - sin x 2 cosx sinx - 1 1 sin2x 2 + sin x 2 - sin x 2 = cosx (cosx – sinx) cosx sinx - 1 cos x 2 1 2 sin x 2 1 2
105. cos2x 1 + tanx cotx - 1 = cos2x 1 + tanx cos2x 1 + tanx cos2x = = - sinxcosx + sin x 2 - = + 1 + tanx cos2x 1 sin2x 2 + sin x 2 - sin x 2 cosx sinx - 1 1 sin2x 2 + sin x 2 - sin x 2 = cosx (cosx – sinx) cosx sinx - 1 cos x 2 sin x 2 sinxcosx 1 2 1 2 - sinxcosx cosx sinx - 1 cos x 2 sin x 2 - sinxcosx sinxcosx 1 2 1 2 - sinxcosx -
106. cos2x 1 + tanx cotx - 1 = cos2x 1 + tanx cos2x 1 + tanx cos2x = = - sinxcosx + sin x 2 - = + 1 + tanx cos2x 1 sin2x 2 + sin x 2 - sin x 2 cosx sinx - 1 1 sin2x 2 + sin x 2 - sin x 2 = cosx (cosx – sinx) cosx sinx - 1 cos x 2 sin x 2 sinxcosx 1 2 1 2 - sinxcosx cosx sinx - 1 cos x 2 sin x 2 - sinxcosx sinxcosx 1 2 1 2 - sinxcosx - cosx sinx - 1 = 1 - 2sinxcosx
107. cos2x 1 + tanx cotx - 1 = cos2x 1 + tanx cos2x 1 + tanx cos2x = = - sinxcosx + sin x 2 - = + = 1 - 2sinxcosx sin2x 1 + tanx cos2x 1 sin2x 2 + sin x 2 - sin x 2 cosx sinx - 1 1 sin2x 2 + sin x 2 - sin x 2 = cosx (cosx – sinx) cosx sinx - 1 cos x 2 sin x 2 sinxcosx 1 2 1 2 - sinxcosx cosx sinx - 1 cos x 2 sin x 2 - sinxcosx sinxcosx 1 2 1 2 - sinxcosx - cosx sinx - 1 = 1 - 2sinxcosx cosx sinx - 1 cosx sinx - 1 = 1 - cosx sinx - 1 = 1 -