Question

How can I sketch the graph of y=3 sin2x and write down the period and amplitude?

Answer 1

To sketch the graph of the function $y=3\sin (2x)$, you can follow these steps:

1. Determine the period: The period of the function $y=\sin (x)$ is $2\pi$, but when there is a coefficient in front of $x$, it affects the period. In this case, the coefficient of $x$ is 2. To find the new period, divide the original period ($2\pi$) by the coefficient: $2\pi /2=\pi$. So the period of $y=3\sin (2x)$ is $\pi$.

2. Determine the amplitude: The coefficient in front of the sine function ($3$ in this case) affects the amplitude. The amplitude is the absolute value of this coefficient, so the amplitude of $y=3\sin (2x)$ is $|3|=3$.

3. Identify key points: Since the period is $\pi$, you can choose a few values of $x$ within that range to plot the graph. For example, you can choose $x=0$, x=π4x = frac{pi}{4}x=4</