# How do you find the period of y = 5 sin(4x−2)−3?

Apr 27, 2016

I found: $\text{period} = \frac{\pi}{2}$ radians.

#### Explanation:

The period of your $\sin$ function can be found observing the number multiplying the $x$ in the argument: in this case the argument of the $\sin$ is: $\left(4 x - 2\right)$ so that the important number will be $4$.
It is important because it is connected to the period $T$ as:
$4 = \frac{2 \pi}{T}$
rearranging you get that:
$T = \frac{2 \pi}{4} = \frac{\pi}{2}$ meaning that your curve will repeat itself every $\frac{\pi}{2}$ radians:
Graphically you can see this as:
graph{5sin(4x-2)-3 [-20.28, 20.26, -10.14, 10.14]}
Try using the $x$ positions two consecutive peaks and see if their spacing is $\frac{\pi}{2}$.