Thus, the ratio is $ \boxed\frac\pi6 $.Question: A plant biologist is modeling the growth pattern of a genetically modified crop using the function $ f(t) = A \cos(\omega t + \phi) $, where $ t $ represents time in days. If the maximum rate of change of growth occurs at $ t = \frac\pi4\omega $ and equals $ 5A\omega $, find the value of $ A $ given that $ \cos(\phi) = \frac35 $ and $ \sin(\phi) = \frac45 $. - Veritas Home Health