Since you say you "don't know how to find \(c\)", that implies that you have found \(a\) and \(b\). Assuming that's the case then you can use this information to solve for \(c\) by setting up equations from the given points:
\(\displaystyle a \cdot \sin(b[1 - 0.5]) + c = 3.5\)
\(\displaystyle a \cdot \sin(b[2 - 0.5]) + c = 0.5\)
Note that I've cleared up what I'm sure is a typo (as the function exactly as you wrote it is just a straight line).
Personally, I wouldn't bother with equations.
In this case, c represents the height about which the curve oscillates, or the vertical translation of the original y=sin(x) graph.
Reading it off the graph, c=2.
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