I need to make this specific wave (A) pattern infinite for a website. I'm trying to get it together, change the anchor points and I'm not having success. How can I do it in the simplest way?
On the top there's a green curve which resembles your orange path. It will not look seamless when duplicated and placed at the end of the first one. For fixing I drew a red horizontal line starting from the left end of the curve. Hold shift to get it exactly horizontal and have Smart guides and Snap to Point ON for exact placement of the starting point.
Fix the curve with the direct selection tool (=white arrow). Move the end point of the curve to the line. Adjust the handles of the endpoints parallel with the line. Convert the endpoints of the curve to smooth anchors with the anchor type conversion tool if they happen to be corner points.
In the bottom the curve is duplicated and the duplicate is placed at the end of the 1st piece. It looks much more continuous than the original although it's still not perfect in mathematics.
What's wrong? If it was a roller coaster the passengers would feel a thump because the centrifugal force still changes discontinuously at the seam. But the direction changes continuously so there's nothing which would break materials.