Trigonometric Function

A Ferris wheel has a radius of 10 meters and is revolving 6 times each minute (wheel's frequency.) The wheel's center is 12 meters from the ground. If time starts on the ground, then find a sine function that shows the height from the ground for a car on the Ferris wheel at any time.

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  1. 6 rotations take 1 minutes
    1 rotation takes 1/6 minutes
    2π/k = 1/6
    k = 12π
    let's start using only amplitude and frequency to get

    height = 10 sin ( 12πt)
    We want to move the curve up 12 units

    height = 10 sin (12πt) + 12

    so now we have to have a horizontal shift so that when t = 0, the height will be 2
    2 = 10 sin 12π(0 + d) + 12
    -1 = sin 12πd
    now we know that sin 3π/2 = -1
    then 12πd = 3π/2
    d = 1/8

    so one version of our graph would be
    height = 10 sin 12π(t + 1/8) + 12

    testing: if t = 1/12, we should be at our highest point of 22

    if t = 1/24
    height = 10 sin 12π(1/12+1/8) + 12
    =10 sin 12π(5/24) + 12
    = 10 sin 5π/2 + 12
    = 10(1) + 12
    = 22

    confirmation here:
    http://www.wolframalpha.com/input/?i=y+%3D+10+sin+%2812π%28t+%2B+1%2F8%29%29+%2B+12++for+0+%3C+t+%3C+.166666

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