Choose trig functions to model periodic phenomena using amplitude, frequency, and midline.
Interpret every sinusoidal parameter with units
Problem
Use the graph of \(h(t)~=~4\sin((\pi~/6)t)~+~10\) to state the amplitude, midline, period, frequency, phase shift, range, and behavior at \(t~=~0\), with units.
Match the equation to standard sinusoidal form before interpreting any parameter. The outside coefficient and constant control amplitude, midline, and vertical range; the inside coefficient and shift control cycle length, rate, and timing. Attach output units to vertical features, input units to period and phase shift, and cycles per input unit to frequency, then check the initial phase and direction.
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