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6.6.handout.model.with.trig.fns

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

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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 * k is the number of cycles in 2 π radians, when the period = 2 k π * 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
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