find an equation for the graph shown to the right.\ntype the equation in the form ( y = a sin (omega x) ) or…

find an equation for the graph shown to the right.\ntype the equation in the form ( y = a sin (omega x) ) or ( y = a cos (omega x) ).\n( y=square )\n(type an exact answer, using ( pi ) as needed. use integers or fractions for any\nnumbers in the expression.)

find an equation for the graph shown to the right.\ntype the equation in the form ( y = a sin (omega x) ) or ( y = a cos (omega x) ).\n( y=square )\n(type an exact answer, using ( pi ) as needed. use integers or fractions for any\nnumbers in the expression.)

Answer

Explanation:

Step1: Determine the amplitude (A)

The amplitude (A) is the maximum distance from the mid - line to the peak (or trough). Since the maximum value is (\frac{1}{3}) and the minimum value is (-\frac{1}{3}), (A=\frac{1}{3}).

Step2: Determine the period (T)

The period (T) is the length of one full cycle. From the graph, (T = 1).

Step3: Calculate the angular frequency (\omega)

The formula for the period of a sine or cosine function is (T=\frac{2\pi}{\omega}). Given (T = 1), we solve for (\omega): [ \begin{align*} 1&=\frac{2\pi}{\omega}\ \omega&=2\pi \end{align*} ]

Step4: Check if it is a sine or cosine function

The graph passes through the origin ((0,0)). The general form of a sine function (y = A\sin(\omega x)) passes through ((0,0)) (since (y(0)=A\sin(0) = 0)), while the general form of a cosine function (y=A\cos(\omega x)) has (y(0)=A). So, the function is a sine function.

Answer:

(y=\frac{1}{3}\sin(2\pi x))