Final answer:
The symmetries in a periodic signal like a sine function include translational symmetry, and possibly even or odd symmetry, depending on how it repeats or mirrors across time or space. Nodes and antinodes also reflect symmetry in wave superpositions.
Step-by-step explanation:
The question refers to symmetries in periodic signals, specifically a periodic signal x(t) that repeats after periodic intervals. Symmetry in signals can refer to even symmetry (mirror symmetry) or odd symmetry (rotational symmetry). In the context given with sin functions from physics, if the function repeats itself at regular intervals, such as every 2π for a sine wave, it is said to have translational symmetry. Additionally, if flipping the function in time or space results in the same function, it may possess even or odd symmetry.
For a sine wave, nodes and antinodes can indicate points of symmetry as well. Nodes are points where the resulting wave at certain positions is always zero regardless of time, and antinodes are points where the wave exhibits maximum amplitude. When considering superposition of waves, phase shifts between two sine waves can alter the symmetry and change the resultant wave's properties like amplitude or frequency.