What is the period of f(t)=sin(t /14)+cos((t)/21)

Leila Jennings

Leila Jennings

Answered question

2022-07-21

What is the period of f ( t ) = sin ( t 14 ) + cos ( t 21 )?

Answer & Explanation

Bianca Chung

Bianca Chung

Beginner2022-07-22Added 16 answers

The period for both sin kt and cos kt is 2 π k
The periods of the two separate oscillations in f(t) are 28 π and 42 π
The period for the compounded oscillation is such that 28 M = 42 N, for lowest positive integers M and N. Easily, M =3 and N = 2. These give the LCM common value 84 π as the period for f(t).
f ( t + 84 π ) = sin ( t 14 + 6 π ) + cos ( t 21 + 4 π ) = sin ( t 14 ) + cos ( t 21 ) = f ( t )

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