find the amplitude, period, and frequency of the sinusoidal function.\nsimplify any fractions.\namplitude =…

Explanation:

Step1: Find the amplitude

The amplitude of a sinusoidal function is half the distance between the maximum and minimum values. The maximum value (y_{max} = 7) and the minimum value (y_{min}=3). Amplitude (A=\frac{y_{max}-y_{min}}{2}=\frac{7 - 3}{2}) [A = 2]

Step2: Find the period

The period is the length of one full cycle of the sinusoidal function. From the graph, we can see that one full cycle occurs over an interval of length (\pi). So, period (T=\pi)

Step3: Find the frequency

The frequency (f) is the reciprocal of the period. Since (T=\pi), then (f=\frac{1}{T}) [f=\frac{1}{\pi}]

Answer:

amplitude (= 2) period (=\pi) frequency (=\frac{1}{\pi})