# How do you determine the amplitude, period, and shifts to graph y = Sin (300t) ?

Jun 26, 2018

$A = | 1 | = 1$
$T = \frac{2 \pi}{300} = \frac{\pi}{150}$
$\text{horizontal shift} = 0$
$\text{vertical shift} = 0$

($A$ is amplitude, $T$ is period)

#### Explanation:

Sinusoidal functions can be written as

$y = a \sin \left(c \left(x - d\right)\right) + b$

where
$| a |$ is the amplitude ($A$)
$b$ is the vertical shift
$\frac{2 \pi}{c}$ is the period ($T$)
$d$ is the horizontal shift.

In this case:
$A = | 1 | = 1$
$T = \frac{2 \pi}{300} = \frac{\pi}{150}$
$\text{horizontal shift} = 0$
$\text{vertical shift} = 0$