Pendulum Ride - Trigonometric Function 1. The problem statement, all variables and given/known data At Canada's Wonderland, a thrill seeker can ride the Xtreme Skyflyer. This is essentially a large pendulum of which the rider is the bob. The height of the rider is given for various times: Time(s) 0 1 2 3 4 5 6 7 8 9 Height(m) 55 53 46 36 25 14 7 5 8 15 Find the amplitude, period, vertical translation, and phase shift for this function. [Note: that the table does not follow the bob through one complete cycle, s 2. Relevant equations y=a sin [b(x-c)] + d 3. The attempt at a solution To find "a" (amplitude)= (max - min) / 2 = (55 - 5)/2 = 25 To find "d" (axis of symmetry)= (max + min) / 2 = (55 + 5)/2 = 30 To find "b" find the Period Period = 2p/absolute value of b However, because this ride works as a pendulum, one cycle will be completed when there are 2 highs and 2 lows. So the bob starts at a height of 55 metres; it will then reach a low of 5 metres; it will (hypothetically) reach a height until it runs out of speed; it will then (hypothetically) return to the minimum height of 5 metres; and then, finally it will return to its start position. That is the completion of 1 cycle in a pendulum. Because the graph is incomplete, we have just one maximum and one minimum. The maximum starts at 55 metres, and then there is a minimum at 5 metres. Therefore, we have only completed 1/4 of the cycle at 7 seconds. Roughly, a complete cycle will take 28 seconds. Therefore Period= 2pie/b which becomes: 28 seconds = 2pie/b 28=360/b b=360/28 b=12.86 So the "b" value is 12.86. To find the value of "c", I will plug in a co-ordinate value into the equation. Let us take the co-ordinate (3, 36) Therefore: y=asin[b(x-c)]+d; becomes: 36=25sin[12.86(3-c)]+30 6=25sin[12.86(3-c)] 6/25=sin[12.86(3-c)] 13.89=12.86(3-c) 1.08=3-c c=3-1.08 c=1.92 And so, my final equation reads as: y=25sin[12.86(x-1.92)]+30 However, when I enter this value into my graphing software, it looks nothing like the graph I did on paper! Do you guys see any errors in what I did? Thank you so much in advance.