What is the period of #f(t)=sin( t / 18 )+ cos( (t)/21 ) #?

2 Answers
A. S. Adikesavan
Aug 11, 2016

#252pi#

Explanation:

The periods dor both sin kt and cos kt is #2pi/k#

Here, the periods of the separate oscillations given by

#sin(t/18) and cos (t/21)# are # 36pi and 42pi#, respectively,

For the compounded oscillation f(t), the period is given by

the period# P = 36 L pi = 42M pi#, for the least pair of positive

integers L and M. So, #P = 252 pi#, against L = 7 and M = 6.

See how it works.

#f(t+252pi)#

#=sin (t/18+14pi)+cos(t/21+12pi)#

#= sin(t/18)+cos(t/21)#

#=f(t)#.

Note that when this P is halved, the first term would change its sign..

Nghi N.
Aug 11, 2016

#252pi#

Explanation:

Period of #sin (t/18)# --> #18(2pi) = 36pi#
Period of #cos (t/21)# --> #21(2pi) = 42pi#
Least common multiple of #36pi and 42pi#
#(36pi)# ... x (7) ---> #252pi#
#(42pi) #...x (6) ---> #252pi#
Period of f(t) --> #252pi#

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