To determine the phase of waves from a diagram, one should analyze the y-intercept where each wave crosses the y-axis, which typically occurs halfway between the origin and the maximum amplitude. The discussion highlights that the sine function reaches half its maximum amplitude at specific angles, notably 30 degrees. Participants suggest that the first wave appears to have a phase of -45 degrees and the second -135 degrees, although these options are not available in the problem. The relationship between the x-intercept and the maximum value is also emphasized, with a reference to the sine function's value at different angles. Understanding these angles and their corresponding sine values is crucial for solving the problem effectively.