The cosine function, denoted as cos(x), is one of the fundamental trigonometric functions. It relates the angle x to the ratio of the length of the adjacent side to the hypotenuse in a right triangle.

The domain of the cosine function is the set of all real numbers, and its range is [-1, 1]. The function is periodic, with a period of 2π radians or 360 degrees. This means that the cosine function repeats its values after every 2π radians or 360 degrees.

To graph the cosine function, we can start by plotting a few key points. For example, at x = 0, the value of cos(0) is 1. At x = π/2 or 90 degrees, the value of cos(π/2) is 0. At x = π or 180 degrees, the value of cos(π) is -1. Continuing this pattern, we can plot other key points such as x = 3π/2, x = 2π, x = 5π/2, and so on.

By connecting these key points with a smooth curve, we obtain the graph of the cosine function. The graph oscillates between the values of -1 and 1, crossing the x-axis at the maximum and minimum points. The amplitude of the cosine graph is 1, and it is centered around the x-axis.