# What is the amplitude and period of y = sin(3x)?

Nov 6, 2016

Amplitude: 1
Period: $\frac{2 \pi}{3}$

#### Explanation:

To determine these features, we need to know what each of the parameters in the functions $y = a \sin b \left(x - c\right) + d$ and $y = a \cos b \left(x - c\right) + d$ mean.

$| a |$ is the amplitude
•The period is given by $\frac{2 \pi}{b}$
•The horizontal transformation is given by $x = c$. For example, if $c = 2$, then the graph has been moved two units right.
•The vertical translation is $y = d$

Using this information to answer the problem above, the function can be written in the form of

$y = 1 \sin \left(3 \left(x\right)\right) + 0$

So, the amplitude is $1$ and the period is $\frac{2 \pi}{3}$. There is no horizontal translation or vertical translation.

Hopefully this helps!