Final answer:
The question deals with Physics concepts such as oscillatory motion, wave functions, nodes, and antinodes, which are common in the High School curriculum.
Step-by-step explanation:
The subject of this question is Physics, specifically dealing with oscillatory motion and wave functions. The student is asked about a particle's position along the x-axis as a function of time, with different equations involving sine and cosine functions describing the position x(t). The antinode and node concepts also appear, which are crucial to understanding standing waves and the interference of waves. Analysis of these functions involves finding specific points in time or space, such as when a particle crosses the origin, or the displacement within a certain time interval, which are typical problems in high school physics courses.