The cosine of 45 degrees can be determined using the unit circle, a fundamental concept in trigonometry. In the unit circle, the radius is 1, and the angle is measured from the positive x-axis.
At 45 degrees, or \\(\frac{\pi}{4}\\) radians, the coordinates of the point on the unit circle are \\((\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2})\\). The cosine function corresponds to the x-coordinate of this point.
Therefore, cos 45 degrees = \\(\frac{\sqrt{2}}{2}\\).
This value is significant because it is a standard angle in trigonometry, and knowing it can help solve various problems involving right triangles and trigonometric functions.