Write a sine function that has a midline of 4, an amplitude of 3 and a period of 2/3

Answer 1

y =A sin(Bx) + D;

A = 3; B = 2π/(2/3) = 3π; D = 4

y = 3sin(3πx) + 4

Answer 2

Of course there are many here that can just supply the answer. More interesting, would be to get you to think about the general form of the sine curve: y = a*sin(bx)+c

Try putting that function into a graphing calculator (desmos.com has a good one). On desmos you can add sliders for a,b,c and see how they affect the function.

Here are some key questions:

1. how is c related to the midline. (do you know what's meant by "midline"?)?
2. how is a related to amplitude?
3. how is b related to period. What even is meant by "period"?

For your question, find a,b and c. That is your answer!