6.6.handout.model.with.trig.fns

6.6.handout.model.with.trig.fns - 6.6 Modeling with...

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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.

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