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

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Answer 1 · 2016-07-29T14:04:37

Period #=3pi#

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.

Answer 2 · 2016-07-29T14:08:25

#3pi#

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#