write the equation of the trigonometric function shown in the graph. \n try \n $y = square\\sin(\\square…

Answer:

$y = 1\sin\left(\frac{1}{2}x\right)+0$

Explanation:

Step1: Determine the amplitude

The amplitude (A) of a sine function (y = A\sin(Bx)+C) is the maximum deviation from the mid - line. The mid - line of the given sine function is (y = 0) (since the graph oscillates symmetrically around (y = 0)). The maximum value of the function is (y = 1) and the minimum value is (y=-1). So, (A=\frac{\text{Max}-\text{Min}}{2}=\frac{1 - (-1)}{2}=1).

Step2: Determine the period and (B)

The period (T) of a sine function (y=\sin(Bx)) is given by (T=\frac{2\pi}{B}). Looking at the graph, the period (T = 4\pi). Using the formula (T=\frac{2\pi}{B}), we substitute (T = 4\pi) into it: (4\pi=\frac{2\pi}{B}). Solving for (B), we cross - multiply to get (4\pi B=2\pi), then (B=\frac{2\pi}{4\pi}=\frac{1}{2}).

Step3: Determine the vertical shift (C)

The vertical shift (C) of a sine function (y = A\sin(Bx)+C) is the mid - line of the function. Since the mid - line of the given function is (y = 0), (C = 0).

So the equation of the trigonometric function is (y = 1\sin\left(\frac{1}{2}x\right)+0).