write the equation of the trigonometric function shown in the graph.\n\n$y=squarecos(square x)+square$

Explanation:

Step1: Find the amplitude

The general form of a cosine function is (y = A\cos(Bx)+C). The amplitude (A) is half the distance between the maximum and minimum values. The maximum value of the dotted - line (auxiliary cosine - like function) is (y = 5) and the minimum is (y = 1). So, (A=\frac{5 - 1}{2}=2).

Step2: Find the period

The period (T) of a cosine function (y=\cos(Bx)) is given by (T=\frac{2\pi}{B}). For the dotted - line (auxiliary cosine - like function), from (x = 0) to (x = 2\pi), the function completes one full cycle. So, (T = 2\pi). Using the formula (T=\frac{2\pi}{B}), we substitute (T = 2\pi) and get (B = 1).

Step3: Find the vertical shift

The vertical shift (C) is the mid - value of the maximum and minimum of the function. (C=\frac{5 + 1}{2}=3).

Answer:

(y = 2\cos(x)+3)