Question

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.