Write a sine function that has a midline of y, equals, 3, y=3, an amplitude of 2 and a period of 4π.
A sine function with a midline of y = 3, an amplitude of 2, and a period of 4π can be represented as:
f(x) = 2sin(x - π) + 3
Explanation:
- The midline of y = 3 means that the graph's horizontal center is at y = 3.
- The amplitude of 2 indicates that the maximum & minimum values of the function are 2 units above and below the midline.
- The period of 4π tells us that one complete cycle of the graph occurs over a distance of 4π units along the x-axis.
- The x - π term represents the horizontal shift that slides the graph to the right by π units. It helps align the starting point of the graph at x = 0.
- Finally, adding 3 ensures that the minimum value of the function reaches the midline at the point y = 3.