What is the period of f(t)=sin( t /13 )+ cos( (13t)/24 ) ?

2 Answers
Jun 11, 2018

The period is =4056pi

Explanation:

The period T of a periodic functon is such that

f(t)=f(t+T)

Here,

f(t)=sin(1/13t)+cos(13/24t)

Therefore,

f(t+T)=sin(1/13(t+T))+cos(13/24(t+T))

=sin(1/13t+1/13T)+cos(13/24t+13/24T)

=sin(1/13t)cos(1/13T)+cos(1/13t)sin(1/13T)+cos(13/24t)cos(13/24T)-sin(13/24t)sin(13/24T)

As,

f(t)=f(t+T)

{(cos(1/13T)=1),(sin(1/13T)=0), (cos(13/24T)=1),(sin(13/24T)=0):}

<=>, {(1/13T=2pi),(13/24T=2pi):}

<=>, {(T=26pi=338pi),(T=48/13pi=48pi):}

<=>, T=4056pi

Jun 11, 2018

624pi

Explanation:

Period of sin (t/13) --> 13(2pi) = 26pi
Period of cos ((13t)/24) --> ((24)(2pi))/13 = (48pi)/13
Period of f(t) --> least common multiple of 26pi and (48pi)/13

26pi .... x (24).............--> .624pi
(48pi)/13 .....x (13)(13)...--> 624pi...-->
Period of f(t) --> 624pi