# What is the period and frequency for sin(2pi t / 5)?

Aug 23, 2015

period of $\sin \left(\frac{2 \pi}{5} t\right) = 5$

frequency of $\sin \left(\frac{2 \pi}{5} t\right) = \frac{1}{5}$

#### Explanation:

$\sin \left(\theta\right)$ has a period of $2 \pi$ relative to $\theta$

$\Rightarrow \sin \left(\frac{2 \pi}{5} t\right)$ has a period of $2 \pi$ relative to $\frac{2 \pi}{5} t$

$\Rightarrow S \in \left(\frac{2 \pi}{5} t\right)$ has a period of $\frac{2 \pi}{\frac{2 \pi}{5}} = 5$ relative to $t$

frequency is the reciprocal of period