# What is the period of f(t)=sin(4t)+cos(24t)

Alessandra Cummings 2022-10-17 Answered
What is the period of $f\left(t\right)=\mathrm{sin}\left(4t\right)+\mathrm{cos}\left(24t\right)$?
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## Answers (1)

exalantaswo
Answered 2022-10-18 Author has 14 answers
The period of both $\mathrm{sin}kt$ and $\mathrm{cos}kt$ is $\frac{2\pi }{k}$. So,
the period ${P}_{1}$ of $\mathrm{cos}24t$ is $\frac{\pi }{12}$ and
the period ${P}_{2}$ of $\mathrm{sin}4t=\frac{\pi }{2}=6{P}_{1}$. And so,
the period of the compounded oscillation
$f\left(t\right)=\mathrm{sin}4t+\mathrm{cos}24t$,
$P={P}_{2}=\frac{\pi }{2}=6{P}_{1}$
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