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5Question: A materials scientist is modeling the thermal expansion of a composite material using the function
to represent the dimensional change over temperature $ x $ (in radians). Find the maximum value of $ f(x) $ over all real numbers $ x $.
To find the maximum value of the function
we use the identity for combining sine and cosine into a single sinusoidal function. Specifically, for any expression of the form
Here, $ a = 3 $ and $ b = 4 $, so the maximum value is
Thus, the maximum value of $ f(x) $ is
Question: An entomologist is analyzing the angular orientation of a pollinators flight path relative to a flower, modeled by the equation
We are given the trigonometric equation:
We rewrite the left-hand side as a single cosine function using the identity:
Question: A science administrator is evaluating a proposal involving two directional light beams modeled as vectors