What is the period of f(t)=sin(t /12)+cos((t)/21)

ajakanvao

ajakanvao

Answered question

2022-11-04

What is the period of f ( t ) = sin ( t 12 ) + cos ( t 21 )?

Answer & Explanation

Cindy Mercer

Cindy Mercer

Beginner2022-11-05Added 13 answers

The period for both sin kt and cos kt is 2 π k
Here, the separate periods of oscillation of the waves
sin ( t 12 ) and cos ( t 21 ) are 24 π and 42 π
So, the period for the compounded oscillation for the sun is the
L C M = 168 π
You see how it works.
f ( t + 168 π ) = sin ( ( 1 12 ) ( t + 168 π ) ) + cos ( ( 1 21 ) ( t + 168 π ) )
= sin ( t 12 + 14 π ) + cos ( t 21 + 8 π )
= sin ( t 12 ) + cos ( t 21 )
=f(t)

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