y = -3 cos ((x/3) + (pi/7). Find the period. Is it 3pi?

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y = -3 cos ((x/3) + (pi/7). Find the period. Is it 3pi?

Mathematics
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For a function of a wave, \[f(x)=A\cos(Bx+C)\] The period of the wave is given \[T=\frac{2\pi}{B}\]
Think of it as anologous to equation of time-varying displacement of a wave \[y(t)=A\cos(\omega t+\alpha)\] \[\omega\] is the angular frequency, and we know that \[\omega=\frac{2\pi}{T}\]\[\implies T=\frac{2\pi}{\omega}\]
But what is w in this case?

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\[f(x)=-3\cos(\frac{1}{3}x+\frac{\pi}{7})\] Compare it to \[f(x)=A\cos(Bx+C)\] What do you think your B is?
1/3?
yep! now your job is as simple as finding \[T=\frac{2\pi}{B}\]
That would be 6pi
Absolutely, solved!
Thanks!

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