# What is the period of f(t)=sin(t /36)+cos((t)/9)

What is the period of $f\left(t\right)=\mathrm{sin}\left(\frac{t}{36}\right)+\mathrm{cos}\left(\frac{t}{9}\right)$?
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Franklin Frey
The period for both $\mathrm{sin}$ kt and $\mathrm{cos}$ kt is $2\frac{\pi }{k}$
The period of $\mathrm{sin}\left(\frac{t}{36}\right)=72\pi$
The period of $\mathrm{cos}\left(\frac{t}{9}\right)=18\pi$
18 is a factor of 72.
So, the period for the compounded oscillation is $72\pi$