Question

# How do you find the amplitude and period of a function y=sin(3x)?

How do you find the amplitude and period of a function y=sin(3x)?

Answer 1

The amplitude measures the distance between the peaks of your function. Since the sine of a number is always bounded between $- 1$ and $1$, and the amplitude is actually half of that distance, the amplitude is $1$.

As for the period, you have that your variable is not $x$ but $3 x$. This means that, in a sense, the variable runs at three times the speed, and so it takes one third of the normal period, which means $\frac{2 \pi}{3}$.
Otherwise, you can use the formula which states that the period of a function like
$A \sin \left(\omega x + \phi\right)$ is $\frac{2 \pi}{\setminus} \omega$.

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