Write a sine function that has a midline of y=5 an amplitude of 4,a period of pi and a horizontal shift of (pi )/(3) to the right. Answer Attemptiout of 2 f(x)=

To write a sine function with the given parameters, we need to consider the following:<br /><br />1. Midline: The midline is the horizontal line that divides the graph of the function into two equal parts. In this case, the midline is $y=5$, which means the function will be centered around this line.<br /><br />2. Amplitude: The amplitude is the distance between the midline and the maximum or minimum value of the function. In this case, the amplitude is 4, which means the function will reach a maximum value of $5+4=9$ and a minimum value of $5-4=1$.<br /><br />3. Period: The period is the distance between two consecutive points where the function repeats itself. In this case, the period is $\pi$, which means the function will repeat every $\pi$ units.<br /><br />4. Horizontal shift: A horizontal shift moves the graph of the function left or right. In this case, the function is shifted $\frac{\pi}{3}$ to the right, which means we need to subtract $\frac{\pi}{3}$ from the input variable $x$.<br /><br />Putting all these together, we can write the sine function as:<br /><br />$f(x) = 4\sin\left(\frac{2\pi}{\pi}(x-\frac{\pi}{3})\right) + 5$<br /><br />Simplifying the expression inside the sine function, we get:<br /><br />$f(x) = 4\sin(2(x-\frac{\pi}{3})) + 5$<br /><br />Therefore, the sine function with the given parameters is:<br /><br />$f(x) = 4\sin(2(x-\frac{\pi}{3})) + 5$