ANSWER and EXPLANATION
(A) The amplitude of the function is half the difference between the maximum and minimum value of the function.
Hence, the amplitude is:
[tex]\begin{gathered} A=\frac{210-10}{2} \\ A=\frac{200}{2} \\ A=100\text{ ft} \end{gathered}[/tex]
(B) The period is the time taken for one complete cycle. From the graph, the period is 90 seconds.
Hence, the value of b is:
[tex]\begin{gathered} b=\frac{2\pi}{period} \\ b=\frac{2\pi}{90} \\ b=\frac{\pi}{45} \end{gathered}[/tex]
(C) The phase shift of the graph is the distance between the vertical axis and the start point of the graph. The graph is a cosine graph, hence, the start point is its peak.
Hence, the phase shift is:
[tex]c=30[/tex]
(D) The midline value of the graph is given to be:
[tex]110[/tex]
(E) The general form for the equation of a cosine function is:
[tex]y=A\cos(bx+c)+d[/tex]
where A = amplitude
b = periodicity
c = horizontal shift
d = vertical shift/midline
Hence, the equation of the cosine function is:
[tex]y=100\cos(\frac{\pi}{45}x+30)+110[/tex]
