What is the primary difference between a sine graph and a cosine graph?

The primary difference between a sine graph and a cosine graph lies in their starting points, which is often described in terms of phase shift. The sine function, represented mathematically as (\sin(x)), starts at 0 when (x = 0). In contrast, the cosine function, represented as (\cos(x)), begins at its maximum value of 1 when (x = 0). This can be interpreted as the sine graph being a cosine graph shifted to the right by 90 degrees, or (\frac{\pi}{2}) radians. Therefore, the correct choice reflects this fundamental relationship between the two graphs.

While both graphs oscillate with the same frequency and have the same amplitude (ranging from -1 to 1), they do not start at the same vertical position at (x = 0). Regarding positivity, cosine values can be negative depending on the input angle, and both graphs have a maximum of 1, however, the sine graph specifically reaches its maximum of 1 at (x = \frac{\pi}{2}), not at (x = 0). This reinforces why the correct answer highlights the phase shift between the sine and cosine graphs.