When cos x equals 1, which of the following values apply?

When taking into account the values of ( x ) for which ( \cos x = 1 ), it's essential to understand the behavior of the cosine function on the unit circle. The cosine of an angle corresponds to the x-coordinate of a point on the unit circle.

The cosine function equals 1 at specific points where the angle ( x ) is a multiple of ( 360^\circ ), which corresponds to the position on the unit circle where the point is (1, 0). Thus, the general solution can be expressed as:

[

x = 360n \quad (n \in \mathbb{Z})

]

This means that the angle can be any integer multiple of ( 360^\circ ), leading to the specific angles of ( 0^\circ ), ( 360^\circ ), etc. Negative multiples of ( 360^\circ ) like ( -360^\circ ) also lead to the same point on the unit circle.

The answer accurately identifies that both ( 0 ) and ( ±360 ) yield ( \cos x = 1 ). In contrast, angles such as ( ±90^\circ ) or ( ±270^\circ )