To find the coordinates of points A and B on the graph of $y = \cos(x^\circ)$ for $-360^\circ \leq x \leq 360^\circ$, we need to analyze the graph provided. Based on the typical shape of the cosine curve, we can determine:

1. Point A: This appears to be a point where the cosine graph crosses the positive $x$-axis. Typically, for $y = \cos(x^\circ)$, the cosine function equals zero at $x = 90^\circ$ and $x = 270^\circ$, depending on the range. However, from the image, point A seems to be positioned at $(360^\circ, 1)$, as it marks the rightmost peak of the cosine wave.

   Therefore, the coordinates of A are approximately $A(360^\circ, 1)$.

2. Point B: This is the point where the cosine graph reaches its minimum, which typically occurs at $x = 180^\circ$ for the cosine function. Visually, it seems that point B represents the lowest part of the wave in the negative region of the $y$-axis. From the typical behavior of $\cos(x^\circ)$, the minimum value of the cosine function is $-1$ at $x = 180^\circ$.

   Therefore, the coordinates of B are approximately $B(180^\circ, -1)$.

Would you like further clarification or additional details about how the cosine function behaves over different intervals?

Here are five follow-up questions to deepen your understanding:

1. What is the general shape of the cosine function, and how does it compare to the sine function?
2. How do the amplitude and period affect the shape of the graph of $y = \cos(x^\circ)$?
3. Can you explain the significance of the points where the graph crosses the x-axis?
4. How do transformations such as horizontal or vertical shifts affect the cosine graph?
5. What is the mathematical formula for determining the period of a cosine function?

Tip: When analyzing trigonometric graphs, pay attention to key points like the maxima, minima, and zero crossings. These can help you quickly determine the behavior of the function over a given interval.