anonymous
  • anonymous
what is the amplitude of the sinusoid by y = -4cos(2x) ? Please try and do a step by step. Literally have no idea how to solve this D:
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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precal
  • precal
when you graph this, the amplitude tell you how far it goes up and down from the midline.
precal
  • precal
take the absolute value of the number in front of cosine
terenzreignz
  • terenzreignz
Brilliant :) Let's start with the general form of the sinusoid, shall we? \[\Large \color{red}a \cos(\color{green}px + \color{blue}b)+\color{orange}q\]

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precal
  • precal
|dw:1371126752520:dw|
terenzreignz
  • terenzreignz
Note that in this example, you can replace the cos with sin, it doesn't really change the nature of these values :)
precal
  • precal
a is your amplitude, just always take the absolute value of a
terenzreignz
  • terenzreignz
^That it is :) As precal has mentioned, the amplitude is the 'height' of your graph (WARNING: This is NOT always the highest value that y could take. See "Vertical Shift" for details) To get the amplitude once your sinusoid is of this form... \[\Large \color{red}a \cos(\color{green}px + \color{blue}b)+\color{orange}q\] As @precal has already mentioned, the amplitude is given by \[\Large |\color{red}a|\]
terenzreignz
  • terenzreignz
Sooner or later, you might be asked for what's called the PERIOD of the sinusoid. Period is how long (on the x-axis) before your sinusoid begins to REPEAT itself. The period itself is given by this expression: \[\Large \frac{2\pi}{\color{green}|p|}\]
precal
  • precal
I believe I stated that the amplitude is the distance of how far and how low the function is from the midline
precal
  • precal
q is your midline in this case it is zero
terenzreignz
  • terenzreignz
Warning wasn't meant to correct you @precal :) It was for the OP
precal
  • precal
|dw:1371127074949:dw|
precal
  • precal
no offense taken, just stating the basics so that the asker can learn how to eventually graph cosine and sine functions
terenzreignz
  • terenzreignz
I'd go on with shifts... as long as @rintintin makes his/her presence felt... But then again, maybe that's too much information.... @rintintin ?
anonymous
  • anonymous
This actually helped a lot. I had no idea how to solve this but both of your explanations helped! I appreciate both of your replies very much!
terenzreignz
  • terenzreignz
Oh, you're here... LOL No problem :)
anonymous
  • anonymous
I was writing it down on a note pad haha.
terenzreignz
  • terenzreignz
Well, if anything's vague, hazy, or unclear in any manner, give me a holler :D
anonymous
  • anonymous
Gotcha! Thanks again.
precal
  • precal
yw

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