Choose trig functions to model periodic phenomena using amplitude, frequency, and midline.
Predict an output value from a sine or cosine model
Problem
Use the model \(h(t)=4\sin((\pi/6)t)+10\) to predict the value at \(t=3\).
Big Picture
What this problem is really about
Evaluate a sinusoidal model from the inside out. Substitute the requested input, simplify the entire angle, find the exact trig value, and only then apply the outside scale and vertical shift. A cycle-position check can confirm the arithmetic: locate the input as a fraction of the period from the model's phase anchor and compare the expected height relative to the midline.
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