Choose trig functions to model periodic phenomena using amplitude, frequency, and midline.
Write a cosine model from amplitude or extreme values, period, midline, and the x-value of a maximum or minimum
Problem
Write a cosine model with amplitude \(4\), period \(12\), midline \(y~=~7\), and a maximum at \(x~=~0\). Use the diagram to check the extreme and period.
An extreme is a natural phase anchor for a cosine model. The sign of the cosine coefficient determines whether that anchor is a maximum or minimum, while its magnitude gives the amplitude and the outside constant gives the midline. Convert period to angular coefficient using a full turn per cycle, then verify the anchored extreme and one complete repeat.
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