Question

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

Answer 1

For a function of a wave,
\[f(x)=A\cos(Bx+C)\]
The period of the wave is given
\[T=\frac{2\pi}{B}\]

Answer 2

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
\[\omega=\frac{2\pi}{T}\]\[\implies T=\frac{2\pi}{\omega}\]

Answer 3

But what is w in this case?

Answer 4

\[f(x)=-3\cos(\frac{1}{3}x+\frac{\pi}{7})\]
Compare it to
\[f(x)=A\cos(Bx+C)\]
What do you think your B is?

Answer 5

1/3?

Answer 6

yep!
now your job is as simple as finding
\[T=\frac{2\pi}{B}\]

Answer 7

That would be 6pi

Answer 8

Absolutely, solved!

Answer 9

Thanks!