Question

trig/pre-calc
amplitude
graph each function on the given interval.

1. ( y = 3 sin x ), ( 0 leq x leq 2 pi )

Explanation:

Step1: Determine the amplitude

The general form of a sine function is \(y = A\sin(x)\), where \(A\) is the amplitude. For \(y = 3\sin(x)\), \(A = 3\).

Step2: Find key points

For \(y=\sin(x)\), key points in the interval \([0, 2\pi]\) are \((0,0)\), \((\frac{\pi}{2},1)\), \((\pi,0)\), \((\frac{3\pi}{2}, - 1)\), \((2\pi,0)\).
For \(y = 3\sin(x)\), multiply the \(y\) - values by \(3\). So the key points are \((0,0)\), \((\frac{\pi}{2},3)\), \((\pi,0)\), \((\frac{3\pi}{2},-3)\), \((2\pi,0)\).

Step3: Plot the points and draw the graph

Plot the points \((0,0)\), \((\frac{\pi}{2},3)\), \((\pi,0)\), \((\frac{3\pi}{2},-3)\), \((2\pi,0)\) on the coordinate plane and connect them with a smooth curve.

Answer:

Graph the function \(y = 3\sin(x)\) in the interval \([0,2\pi]\) by plotting the key points \((0,0)\), \((\frac{\pi}{2},3)\), \((\pi,0)\), \((\frac{3\pi}{2},-3)\), \((2\pi,0)\) and drawing a smooth sine - wave curve through them.