Question

standard 15 homework
score: 0/21 answered: 0/20
question 1
sketch a graph of the function $f(x)=\sin(x)$.
clear all draw:
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Explanation:

Step1: Identify 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 the points

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

Step3: Draw the curve

Connect these points with a smooth curve. The function \(y = \sin(x)\) is a periodic function with period \(T = 2\pi\), and its graph oscillates between \(y=-1\) and \(y = 1\).

Answer:

The graph of \(y=\sin(x)\) is a sine - wave that passes through the points \((0,0)\), \((\frac{\pi}{2},1)\), \((\pi,0)\), \((\frac{3\pi}{2},-1)\), \((2\pi,0)\) and repeats every \(2\pi\) units.