# What is the amplitude and period of y=5/3sin(-2/3x)?

Apr 28, 2017

$A m p l i t u \mathrm{de} = \frac{5}{3}$
$P e r i o d = 3 \pi$

#### Explanation:

Consider the form $a \sin \left(b x - c\right) + d$

The amplitude is $| a |$

and the period is $\frac{2 \pi}{|} b |$

We can see from your problem that
$a = \frac{5}{3}$ and $b = - \frac{2}{3}$

So for amplitude:

$A m p l i t u \mathrm{de} = | \frac{5}{3} |$ $- - \to$ $A m p l i t u \mathrm{de} = \frac{5}{3}$

and for period:

$P e r i o d = \frac{2 \pi}{|} - \frac{2}{3} |$ $- - \to$ $P e r i o d = \frac{2 \pi}{\frac{2}{3}}$

Consider this as a multiplication for better understanding...

$P e r i o d = \frac{2 \pi}{1} \div \frac{2}{3}$ $- - \to$ $P e r i o d = \frac{2 \pi}{1} \cdot \frac{3}{2}$

$P e r i o d = \frac{6 \pi}{2}$ $- - \to$ $P e r i o d = 3 \pi$