Question

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

Explanation:

Step1: Determine key points

For \(y = \cos(x)\), when \(x = 0\), \(y=\cos(0)=1\); when \(x=\pi\), \(y = \cos(\pi)=- 1\); when \(x = 2\pi\), \(y=\cos(2\pi)=1\). The period of \(y = \cos(x)\) is \(T = 2\pi\), and the range is \([-1,1]\).

Step2: Plot the points and draw the curve

Plot the points \((0,1)\), \((\pi,-1)\), \((2\pi,1)\) and other points such as \((\frac{\pi}{2},0)\), \((\frac{3\pi}{2},0)\) on the coordinate plane. Then, connect these points with a smooth curve that oscillates between \(y = 1\) and \(y=-1\) with a period of \(2\pi\).

Answer:

The graph of \(y = \cos(x)\) is a periodic wave - like curve with period \(2\pi\), amplitude \(1\), passing through points \((0,1)\), \((\frac{\pi}{2},0)\), \((\pi,-1)\), \((\frac{3\pi}{2},0)\), \((2\pi,1)\) etc.