Consider The Giant Wheel at Cedar Point again. The Giant Wheel is a circle with diameter 128 feet which sits on an 8 foot tall platform making its overall height 136 feet. It completes two revolutions in 2 minutes and 7 seconds. Assuming that the riders are at the edge of the circle, find a sinusoid which describes the height of the passengers above the ground t seconds after they pass the point on the wheel closest to the ground.

     h(t) = 72 + 64·sin(2π(t -31.75)/127)

Step-by-step explanation:

The generic form will be ...

  h(t) = a +b·sin(c(t -d))

The value of 'a' is the midline of the height function, halfway between the minimum (8) and the maximum (136).

  a = (8 +136)/2 = 144/2 = 72

The value of 'b' is the amplitude of the height function, half the difference between the minimum and the maximum.

  b = (136 -8)/2 = 128/2 = 64

The value of 'c' is the frequency of the motion in radians per second. It will be ...

  c = 2π/(period in seconds) = 2π/127

The value of 'd' is the number of seconds from the minimum (8 ft) until the wheel first reaches the midline. It will be 1/4 of the revolution time:

  d = 127/4 = 31.75

Then our finished sinusoidal function is ...

     h(t) = 72 + 64·sin(2π(t -31.75)/127)

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Additional comment

If we were to use the cosine function instead, the equation could be simpler:

  h(t) = 72 -64·cos(2πt/127)

The cosine already starts at its maximum value, so height will be at a minimum if we use the negative of the cosine function.

why can't you?

step-by-step explanation:

-1/2 +2

step-by-step explanation: