1. The problem is to sketch the graph of the function $y = \sin x$ for $0 \leq x \leq 360^\circ$. 2. The sine function is periodic with period $360^\circ$, and it oscillates between $-1$ and $1$. 3. Important points to plot are at $x = 0^\circ, 90^\circ, 180^\circ, 270^\circ, 360^\circ$ where: - $\sin 0^\circ = 0$ - $\sin 90^\circ = 1$ - $\sin 180^\circ = 0$ - $\sin 270^\circ = -1$ - $\sin 360^\circ = 0$ 4. The graph starts at 0, rises to 1 at $90^\circ$, returns to 0 at $180^\circ$, falls to -1 at $270^\circ$, and returns to 0 at $360^\circ$. 5. The shape is a smooth wave crossing the x-axis at $0^\circ, 180^\circ, 360^\circ$ and reaching maxima and minima at $90^\circ$ and $270^\circ$ respectively. Final answer: The graph of $y = \sin x$ for $0 \leq x \leq 360^\circ$ is a sine wave starting at 0, peaking at 1, dipping to -1, and returning to 0 at $360^\circ$.