MHB 7.8.99 find PS, VS Period, graph

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The discussion focuses on analyzing the function y = cos(x + π/2) to determine its amplitude, period, phase shift (PS), and vertical shift (VS). The amplitude is identified as 1, the period as 2π, and the phase shift as π/2 to the left, with no vertical shift. Participants clarify the definitions of the parameters, noting that the coefficient of x in the cosine function is crucial for determining angular frequency (ω). There is some confusion regarding the notation for vertical shift, with participants discussing variations in terminology across different texts. Overall, the thread emphasizes understanding the properties of trigonometric functions and their graphical representations.
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$\tiny\textbf{7.8.a09 Radford HS}$
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
 
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$y=\cos\left(x + \dfrac{\pi}{2}\right)$

amplitude = 1

period, $T = 2\pi$

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

no vertical shift

fyi, $\cos\left(x+\dfrac{\pi}{2}\right) = -\sin{x}$
 
[math]y = A ~ sin( \omega x + \phi ) + y_0[/math]

What was your [math]\omega[/math] again?

-Dan
 
topsquark said:
[math]y = A ~ sin( \omega x + \phi ) + y_0[/math]

What was your [math]\omega[/math] again?

-Dan

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

try 1
 
karush said:
$y=\cos\left(x+\dfrac{\pi}{2}\right)$
well thot it was 2 maybe 4? it was kinda :unsure:
[math]y = cos \left ( x + \dfrac{ \pi }{2} \right )[/math]

[math]y = A ~ cos( \omega x + \phi ) + y_0[/math]

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

Geez, dude! You are better than that!

-Dan
 
topsquark said:
[math]y = cos \left ( x + \dfrac{ \pi }{2} \right )[/math]

[math]y = A ~ cos( \omega x + \phi ) + y_0[/math]

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
 
karush said:
$y = \cos \left( 1 \left( x + \dfrac{ \pi }{2} \right )\right )$

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
[math]\omega[/math] - angular frequency
[math]\phi[/math] - phase angle, or phase shift as you are calling it
[math]y_0[/math] - vertical displacement, or vertical shift as you are calling it. Some would also call this "h."

-Dan
 

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