Question

1. $y = 3cos x, 0leq xleq 2pi$

Explanation:

Step1: Find key points

For \(y = A\cos x\), the amplitude is \(|A|\). Here \(A = 3\), so amplitude is \(3\).
The standard cosine function \(y=\cos x\) has key points at \(x = 0,\frac{\pi}{2},\pi,\frac{3\pi}{2},2\pi\).
For \(y = 3\cos x\):

• When \(x = 0\), \(y=3\cos(0)=3\times1 = 3\)
• When \(x=\frac{\pi}{2}\), \(y = 3\cos(\frac{\pi}{2})=3\times0 = 0\)
• When \(x=\pi\), \(y=3\cos(\pi)=3\times(- 1)=-3\)
• When \(x=\frac{3\pi}{2}\), \(y = 3\cos(\frac{3\pi}{2})=3\times0 = 0\)
• When \(x = 2\pi\), \(y=3\cos(2\pi)=3\times1 = 3\)

Step2: Plot the points and draw the graph

Plot the points \((0,3),(\frac{\pi}{2},0),(\pi,- 3),(\frac{3\pi}{2},0),(2\pi,3)\) on the coordinate system. Then connect these points with a smooth curve.

Answer:

The graph of \(y = 3\cos x\) for \(0\leq x\leq2\pi\) has amplitude \(3\), passes through the points \((0,3),(\frac{\pi}{2},0),(\pi,-3),(\frac{3\pi}{2},0),(2\pi,3)\) and is a cosine - type curve.