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Unformatted text preview: 7 t, so we (temporarily) write the height in terms of θ as h = 64 sin (θ) + 72.
Subtracting π from θ gives the ﬁnal answer h(t) = 64 sin θ − π + 72 = 64 sin 127 t − π + 72. We
can check the reasonableness of our answer by graphing y = h(t) over the interval 0, 127 .
136 72 8
2 t A few remarks about Example 11.1.1 are in order. First, note that the amplitude of 64 in our
answer corresponds to the radius of the Giant Wheel. This means that passengers on the Giant
Wheel never stray more than 64 feet vertically from the center of the Wheel, which makes sense.
Second, the phase shift of our answer works out to be 4π/127 = 127 = 15.875. This represents the
‘time delay’ (in seconds) we introduce by starting the motion at the point P as opposed to the
point Q. Said diﬀerently, passengers which ‘start’ at P take 15.875 seconds to ‘catch up’ to the
Our next example revisits the daylight data ﬁrst introduced in Section 2.5, Exercise 4b.
4 We are readjusting our ‘baseline’ from y = 0 to y = 72....
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