Aarabi M.

# 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:

By: Tutor
5.0 (66)

Experienced Physics Teacher for Physics Tutoring 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.

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]
Report

08/23/17

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