When cos x = ±1, what are the possible values of x?

The equation cos x = ±1 corresponds to specific angles on the unit circle where the cosine function takes on these values. The cosine of an angle represents the x-coordinate of a point on the unit circle.

When cos x = 1, this occurs at an angle of 0 degrees (or 360 degrees, which wraps around to the same point). In general, when considering cosine, we can also represent it as 2πk for any integer k, which includes 0 and multiples of 360 degrees.

When cos x = -1, this occurs at an angle of 180 degrees (or 540 degrees, which is another multiple of 180 degrees). This can also be expressed as π + 2πk for any integer k, which includes ±180 degrees.

Thus, the possible values of x that satisfy cos x = ±1 are indeed 0 degrees and ±360 degrees for cos x = 1, as well as 180 degrees for cos x = -1, making 0 and ±360 the general solutions. Therefore, the correct options correctly identify the angles corresponding to these cosine values.