1. The problem is to understand the cosine function, denoted as $\cos(x)$.\n\n2. The cosine function is a fundamental trigonometric function defined as the ratio of the adjacent side to the hypotenuse in a right triangle, or on the unit circle as the x-coordinate of a point at an angle $x$ radians from the positive x-axis.\n\n3. Important properties of $\cos(x)$ include:\n- It is periodic with period $2\pi$, meaning $\cos(x) = \cos(x + 2\pi)$.\n- Its range is $[-1,1]$.\n- It has zeros at $x = \frac{\pi}{2} + k\pi$ for any integer $k$.\n- It is an even function: $\cos(-x) = \cos(x)$.\n\n4. The function can be expressed as a power series: $$\cos(x) = \sum_{n=0}^\infty (-1)^n \frac{x^{2n}}{(2n)!}.$$\n\n5. For example, to evaluate $\cos(0)$, substitute $x=0$ into the series or use the unit circle definition: $\cos(0) = 1$.\n\n6. To graph $y = \cos(x)$, plot points for values of $x$ and connect smoothly, noting the wave oscillates between 1 and -1 with zeros at $\frac{\pi}{2}, \frac{3\pi}{2}$, etc.\n\nThis explanation covers the basics of the cosine function and its key properties.