Choose trig functions to model periodic phenomena using amplitude, frequency, and midline.
Write a sine model from maximum and minimum values, period, midline, and the direction of a midline crossing
Problem
Write a sine model with amplitude \(3\), period \(10\), midline \(y~=~4\), and a rising midline crossing at \(x~=~0\). Use the diagram to check the starting direction.
A rising midline crossing is a natural phase anchor for a sine model. Use the amplitude for the vertical scale, the midline for the outside shift, and convert the desired period into an angular coefficient by dividing a full turn by that period. Then test the starting input to confirm both the midline value and the initial direction.
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