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

2 Answers

Period =3pi

Explanation:

The given equation

f(t)=sin ((2t)/3)

For the general format of sine function

y=A*sin(B(x-C))+D

Formula for the period =(2pi)/abs(B)

for f(t)=sin ((2t)/3)

B=2/3

period =(2pi)/abs(B)=(2pi)/abs(2/3)=3pi

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

Jul 29, 2016

3pi

Explanation:

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

Here, f(t+P) = sin ((2/3)(t+P))=sin(2t/3+(2P)/3)

Now, (2P)/3 = 2pi would make

f(t+P) = sin ((2t)/3+2pi)=sin((2t)/3)=f(t).

So, P = 3pi