## a1234 one year ago y = -3 cos ((x/3) + (pi/7). Find the period. Is it 3pi?

1. anonymous

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

2. anonymous

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}$

3. a1234

But what is w in this case?

4. anonymous

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

5. a1234

1/3?

6. anonymous

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

7. a1234

That would be 6pi

8. anonymous

Absolutely, solved!

9. a1234

Thanks!