# What is the period, amplitude, and frequency for the graph f(x) = 1 + 2 \sin(2(x + \pi))?

Dec 6, 2014

The general form of the sine function can be written as

$f \left(x\right) = A \sin \left(B x \pm C\right) \pm D$, where

$| A |$ - amplitude;
$B$ - cycles from $0$ to $2 \pi$ - the period is equal to $\frac{2 \pi}{B}$
$C$ - horizontal shift;
$D$ - vertical shift

Now, let's arrange your equation to better match the general form:

$f \left(x\right) = 2 \sin \left(2 x + 2 \pi\right) + 1$. We can now see that

Amplitude -$A$ - is equal to $2$, period -$B$ - is equal to $\frac{2 \pi}{2}$ = $\pi$, and frequency, which is defined as $\frac{1}{p e r i o d}$, is equal to $\frac{1}{\pi}$.