Aarabi M.

asked • 08/23/17

trigonometry question?

Kevin is riding a mini Ferris wheel. He reaches the maximum height of 9m at 5s and then reaches the minimum height of 1m at 65s.
a.What is the period (the length of time to complete one cycle)?
b.what is the radius of the wheel?
c.sketch one cycle of the function. Label the graph.
d.the corresponding cosine equation:

1 Expert Answer

By:

Arturo O. answered • 08/23/17

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(a)
 
He completes 1 cycle in twice the time it takes to complete half a cycle.  It takes half a cycle to get from the top to the bottom.
 
T = 2(65 - 5) s = 120 s
 
(b)
 
The difference between maximum and minimum heights must equal twice the radius.
 
2r = (9 - 1) m
 
r = 4 m
 
(c)
 
Unable to graph or sketch in this format.
 
(d)
 
I am not clear what you mean by "corresponding cosine equation".
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Arturo O.

Perhaps you meant to find an equation for height as a function of time, using the cosine function?  If so, then
 
h(t) = hmin + r + r cos[ω(t - 5)] = 1 + 4{1 + cos[ω(t - 5)]}
 
h(t) = 1 + 4{1 + cos[ω(t - 5)]},
 
where
 
cos[ω(t - 5)] is the angle measured from the upward vertical radius of the wheel.  The (t - 5) in the  cosine accounts for a head start of 5 seconds at the top.
 
ω = 2π/T = 2π/120 rad/sec = π/60 rad/sec
 
h(t) = 1 + 4{1 + cos[(π/60)(t - 5)]},
 
with t in seconds, the angle in radians, and h in meters.  Test it.
 
Is h(5) = 9 ?
 
h(5) = 1 + 4{1 + cos[(π/60)(5 - 5)]} = 1 + 4(1 + cos0) = 1 + 4(1 + 1) = 9  [good]
 
Is h(65) = 1 ?
 
h(65) = 1 + 4{1 + cos[(π/60)(65 - 5)]} = 1 + 4(1 + cosπ) = 1 + 4(1 -1) = 1  [good]
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08/23/17

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