1. The problem is to sketch the graph of $y = \cos x$ for $0 \leq x \leq 360^\circ$. 2. The cosine function is defined as $y = \cos x$, where $x$ is the angle in degrees. 3. Important properties of $\cos x$: - The range is $[-1, 1]$. - The period is $360^\circ$, meaning the function repeats every $360^\circ$. - Key points are at $0^\circ, 90^\circ, 180^\circ, 270^\circ, 360^\circ$. 4. Evaluate $\cos x$ at key points: - $\cos 0^\circ = 1$ - $\cos 90^\circ = 0$ - $\cos 180^\circ = -1$ - $\cos 270^\circ = 0$ - $\cos 360^\circ = 1$ 5. Plot these points on the Cartesian plane with $x$-axis from $0$ to $360$ degrees and $y$-axis from $-1$ to $1$. 6. Connect the points smoothly to form the wave shape of the cosine function, starting at $1$, decreasing to $0$ at $90^\circ$, down to $-1$ at $180^\circ$, back to $0$ at $270^\circ$, and returning to $1$ at $360^\circ$. This completes the sketch of $y = \cos x$ for $0 \leq x \leq 360^\circ$.