# What is the period of sin (5*x)?

Jan 30, 2016

period$= {72}^{\circ}$

#### Explanation:

The general equation for a sine function is:

$f \left(x\right) = a \sin \left[k \left(x - d\right)\right] + c$

where:
$| a | =$amplitude
$| k | =$horizontal stretch/compression or ${360}^{\circ} / \text{period}$
$d =$phase shift
$c =$vertical translation

In this case, the value of $k$ is $5$. To find the period, use the formula, $k = {360}^{\circ} / \text{period}$:

$k = {360}^{\circ} / \text{period}$

$5 = {360}^{\circ} / \text{period}$

$5 \cdot \text{period} = {360}^{\circ}$

$\text{period} = {360}^{\circ} / 5$

$\text{period} = {72}^{\circ}$

$\therefore$, the period is ${72}^{\circ}$.