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Unformatted text preview: 6.6 Modeling with Trigonometric Functions
The graphs of y = sin θ and y = cos θ can model periodic phenomena when they are transformed to
fit a given situation. The transformed functions have the form y = a sin(k( θ d)) + c or y = a cos(k(
θ d)) + c, where
* a is the amplitude and a = (max – min)/2
2π * k is the number of cycles in 2 π radians, when the period = k
* d gives the horizontal translation (called the phase shift)
* c is the vertical translation and y = c is the equation of the axis.
Example 1
A Ferris wheel with a diameter of 16 m completes one revolution in 40 seconds. The
center of its axle is 12 m above the ground.
a) Model the height, h in meters, above the ground of a rider after boarding the ride at the bottom
of the wheel using a function where t represents time, in seconds. Sketch a graph of the function
for one period. b) Find the rider’s height above the ground 18 seconds into the ride. c) Find the time elapsed when the rider first reaches a height of 6 m above the ground. Verify your
answer using the graph. d) Find the next time when the rider reaches this height of 6 m above the ground. e) Change the equation to reflect that the rider boards the Ferris wheel 6 m above the ground. Example 2 See page 358 in our text for Example 3 ...
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This note was uploaded on 01/14/2012 for the course MAT 107 taught by Professor Sda during the Spring '11 term at Beacon FL.
 Spring '11
 sda

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