# What is the period of f(t)=sin( ( 2t ) /3 ) ?

##### 2 Answers

Period $= 3 \pi$

#### Explanation:

The given equation

$f \left(t\right) = \sin \left(\frac{2 t}{3}\right)$

For the general format of sine function

$y = A \cdot \sin \left(B \left(x - C\right)\right) + D$

Formula for the period $= \frac{2 \pi}{\left\mid B \right\mid}$

for $f \left(t\right) = \sin \left(\frac{2 t}{3}\right)$

$B = \frac{2}{3}$

period $= \frac{2 \pi}{\left\mid B \right\mid} = \frac{2 \pi}{\left\mid \frac{2}{3} \right\mid} = 3 \pi$

God bless.....I hope the explanation is useful.

Jul 29, 2016

$3 \pi$

#### Explanation:

The least positive P (if any), for which f(t+P)=f(t), is the period of f(t).

Here, $f \left(t + P\right) = \sin \left(\left(\frac{2}{3}\right) \left(t + P\right)\right) = \sin \left(2 \frac{t}{3} + \frac{2 P}{3}\right)$

Now, $\frac{2 P}{3} = 2 \pi$ would make

$f \left(t + P\right) = \sin \left(\frac{2 t}{3} + 2 \pi\right) = \sin \left(\frac{2 t}{3}\right) = f \left(t\right)$.

So, $P = 3 \pi$