9..State the changes that are occurring from the pa A) y=sin(1)/(2)(x+(pi )/(3))-2 (worth 11 points)OR

## Step 1<br />The given function is \(y = \sin\frac {1}{2}(x+\frac {\pi }{3})-2\). This function is a transformation of the basic sine function \(y = \sin(x)\).<br /><br />## Step 2<br />The coefficient of \(x\) inside the sine function, which is \(\frac {1}{2}\), is the frequency of the function. The frequency determines how many cycles the function completes in a given interval. In this case, the frequency is \(\frac {1}{2}\), which means the function completes two cycles in the interval \(2\pi\).<br /><br />## Step 3<br />The term \(\frac {\pi }{3}\) inside the sine function is the phase shift of the function. The phase shift determines the horizontal shift of the function. In this case, the phase shift is \(-\frac {\pi }{3}\), which means the function is shifted to the left by \(\frac {\pi }{3}\).<br /><br />## Step 4<br />The term \(-2\) outside the sine function is the vertical shift of the function. The vertical shift determines the vertical shift of the function. In this case, the function is shifted down by 2 units.