# 7.8.99 find PS, VS Period, graph

• MHB
Gold Member
MHB
$\tiny\textbf{7.8.a09 Radford HS}$
Find amplitude, period, PS, VS. then graph.
$y=\cos\left(x+\dfrac{\pi}{2}\right)$

For the graphs of $y=A\sin(\omega x - \phi)$ or $y=A\cos(\omega x - \phi),\omega>0$
Amplitude $=|A|$
Period $T=\dfrac{2\pi}{\omega}=\dfrac{2\pi}{2}=\pi$
PS $=\dfrac{\phi}{\omega}=\dfrac{\pi}{4}$

well so far
I don't know what the greek letter is for VS or Vertical Shift? which is usually D

skeeter
$y=\cos\left(x + \dfrac{\pi}{2}\right)$

amplitude = 1

period, $T = 2\pi$

phase shift = $\dfrac{\pi}{2}$ left

no vertical shift

fyi, $\cos\left(x+\dfrac{\pi}{2}\right) = -\sin{x}$

Gold Member
MHB
$$\displaystyle y = A ~ sin( \omega x + \phi ) + y_0$$

What was your $$\displaystyle \omega$$ again?

-Dan

Gold Member
MHB
$$\displaystyle y = A ~ sin( \omega x + \phi ) + y_0$$

What was your $$\displaystyle \omega$$ again?

-Dan

 $y=\cos\left(x+\dfrac{\pi}{2}\right)$
well thot it was 2 maybe 4? it was kinda :unsure:

skeeter
 $y=\cos\left(x+\dfrac{\pi}{2}\right)$
well thot it was 2 maybe 4? it was kinda :unsure:

try 1

Gold Member
MHB
 $y=\cos\left(x+\dfrac{\pi}{2}\right)$
well thot it was 2 maybe 4? it was kinda :unsure:
$$\displaystyle y = cos \left ( x + \dfrac{ \pi }{2} \right )$$

$$\displaystyle y = A ~ cos( \omega x + \phi ) + y_0$$

What is the coefficient of x in your cosine argument??

Geez, dude! You are better than that!

-Dan

Gold Member
MHB
$$\displaystyle y = cos \left ( x + \dfrac{ \pi }{2} \right )$$

$$\displaystyle y = A ~ cos( \omega x + \phi ) + y_0$$

What is the coefficient of x in your cosine argument??

Geez, dude! You are better than that!

-Dan
 $y = \cos \left( 1 \left( x + \dfrac{ \pi }{2} \right )\right )$ are you using $y_0$ as VS

Gold Member
MHB
 $y = \cos \left( 1 \left( x + \dfrac{ \pi }{2} \right )\right )$ are you using $y_0$ as VS
Yes. There really is no standard way of writing the general cosine equation. It varies from class to class and text to text. (In fact I learned it as sine in College.)

A - wave amplitude
$$\displaystyle \omega$$ - angular frequency
$$\displaystyle \phi$$ - phase angle, or phase shift as you are calling it
$$\displaystyle y_0$$ - vertical displacement, or vertical shift as you are calling it. Some would also call this "h."

-Dan