using your unit circle as a guide, help me graph the function ( y = cos x ).

Explanation:

Step1: Determine key points

On the unit circle, for (y = \cos x), when (x = 0), (y=\cos(0)=1); when (x=\frac{\pi}{2}), (y = \cos(\frac{\pi}{2})=0); when (x=\pi), (y=\cos(\pi)= - 1); when (x=\frac{3\pi}{2}), (y=\cos(\frac{3\pi}{2})=0); when (x = 2\pi), (y=\cos(2\pi)=1).

Step2: Plot the key points

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

Step3: Sketch the curve

Connect these points with a smooth curve. Since the cosine function is periodic with period (T = 2\pi), the pattern repeats every (2\pi) units along the (x) - axis.

Answer:

Plot the points ((0,1)), ((\frac{\pi}{2},0)), ((\pi, - 1)), ((\frac{3\pi}{2},0)), ((2\pi,1)) and connect them with a smooth curve that repeats every (2\pi) units.