# What is the period of f(t)=sin( ( 5 t ) /3 ) ?

Dec 31, 2015

In order to find the period of a trigonometric function, we must equal its argument to $0$ and $2 \pi$, which are the values of the argument which constute a period.

#### Explanation:

Every trigonometric function, as a sine or a cosine, has a period, which is the distance between two consecutive values of $t$.

For sine and cosine, period equals $2 \pi$.

To find the period of a trigonometric function, we must make its argument equal to a period extremes. For example, $0$ and $2 \pi$.

• $\frac{5 t}{3} = 0 \rightarrow {t}_{1} = 0$
• $\frac{5 t}{3} = 2 \pi \rightarrow {t}_{2} = \frac{6}{5} \pi$

So period is $\Delta t = {t}_{2} - {t}_{1} = \frac{6}{5} \pi$.