graph the function f(x) = cos(x).

Explanation:

Step1: Recall key - points of cosine function

The cosine function (y = \cos(x)) has a period of (2\pi), amplitude of (1), and (\cos(0)=1), (\cos(\frac{\pi}{2}) = 0), (\cos(\pi)=- 1), (\cos(\frac{3\pi}{2}) = 0), (\cos(2\pi)=1).

Step2: Plot key - points

Plot the points ((0,1)), ((\frac{\pi}{2},0)), ((\pi,-1)), ((\frac{3\pi}{2},0)), ((2\pi,1)) on the given coordinate grid.

Step3: Sketch the curve

Connect the points with a smooth curve. Since the period is (2\pi), repeat the pattern for (x\in[-2\pi,2\pi]).

Answer:

Sketch a smooth curve passing through ((0,1)), ((\frac{\pi}{2},0)), ((\pi,-1)), ((\frac{3\pi}{2},0)), ((2\pi,1)) and repeating with period (2\pi) on the given grid.