7.8.11 Find amplitude, period, PS, VS. graph 2 periods

[karush]

$\tiny{\textbf{7.8.11 Campbell HS}}$
Find (A)mplitude, (P)eriod, PS, VS. graph 2 periods
$y=3\cos(\pi x-2)+5$

by observation we have A=3 and VS=5
ok assume $\omega=\pi$
so if period is $T=\dfrac{2\pi}{\omega}$ then $T=\dfrac{2\pi}{\pi}=2$

 

[topsquark]

$\tiny{\textbf{7.8.11 Campbell HS}}$
Find (A)mplitude, (P)eriod, PS, VS. graph 2 periods
$y=3\cos(\pi x-2)+5$

by observation we have A=3 and VS=5...
and $\omega=\pi$ ...

Otherwise, good!

-Dan

 

[karush]

ok i think $\phi =2$ then PS is $\dfrac{\phi}{\omega}=\dfrac{2}{\pi}$

really! :unsure:

 

[topsquark]

Okay, check with your general form of the sine wave. I use
\(\displaystyle y = A ~ cos( \omega x + \phi ) + y_0\)

Your source might be using
\(\displaystyle y = A ~ cos( \omega x - \phi ) + y_0\)
in which case, yes, \(\displaystyle \phi = 2\). In this model I'm using \(\displaystyle \phi = - 2\). The negative sign is important because it tells which way the wave has been shifted along the x-axis.

-Dan