What is the period of $f(t)=\mathrm{sin}(4t)+\mathrm{cos}(24t)$?

Alessandra Cummings
2022-10-17
Answered

What is the period of $f(t)=\mathrm{sin}(4t)+\mathrm{cos}(24t)$?

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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

$f(t)=\mathrm{sin}4t+\mathrm{cos}24t$,

$P={P}_{2}=\frac{\pi}{2}=6{P}_{1}$

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

$f(t)=\mathrm{sin}4t+\mathrm{cos}24t$,

$P={P}_{2}=\frac{\pi}{2}=6{P}_{1}$

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