Question

using your unit circle as a guide, help me graph the function $y = \sin x$.

Explanation:

Step1: Determine key points

For \(y = \sin x\), when \(x = 0\), \(y=\sin(0) = 0\); when \(x=\frac{\pi}{2}\), \(y = \sin(\frac{\pi}{2})=1\); when \(x=\pi\), \(y=\sin(\pi)=0\); when \(x=\frac{3\pi}{2}\), \(y=\sin(\frac{3\pi}{2})=- 1\); when \(x = 2\pi\), \(y=\sin(2\pi)=0\).

Step2: Plot key points

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

Step3: Sketch the curve

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

Answer:

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