anonymous
  • anonymous
What are the amplitude, period, phase shift, and midline of f(x) = -3 sin(4x - π) + 2? (5 points)
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
anonymous
  • anonymous
http://gyazo.com/79c729685b340c46e3861aac421894b3
freckles
  • freckles
what do you think the amp is?

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freckles
  • freckles
that is all you really have to know to get this question
anonymous
  • anonymous
how do i find it
freckles
  • freckles
oh I thought you would know how because it is the easiest thing to find it is the absolute value of the constant number being multiplied to the trig function there
anonymous
  • anonymous
so 3?
freckles
  • freckles
yep
freckles
  • freckles
you are done because there is only one option with amp=3
anonymous
  • anonymous
lol yay thanks
anonymous
  • anonymous
http://gyazo.com/0060f7a559b9d1fb6d4bef7b957a2c03 is that answer right
Owlcoffee
  • Owlcoffee
in any trigonometric equality with the form: \[y=Asin(ax+ \alpha) \] The amplitude is the number "A" and you can calculate the period with: \[p=\frac{ 2 \pi }{ a }\]
freckles
  • freckles
you mean the amp=|A|?
freckles
  • freckles
\[y=A \sin(bx+c)+d \\ \text{ amp } =|A| \\ \text{ period } =\frac{2 \pi}{|b|} \\ \\ \text{ phase shift : } \text{ solve for } x : bx+c=0 \\ \text{ max if } A \text{ is } \text{ positive is } A(1)+d=A+d \\ \text{ min if } A \text{ is } \text{ positive is } A(-1)+d=-A+d \\ \text{ so the average the of max and min is }=\frac{(A+d)+(-A+d)}{2}=\frac{2d}{2}=d \\ \text{ the midline is therefore } y=d\]
anonymous
  • anonymous
thank you for all of that
anonymous
  • anonymous
was my answer correct for the other 1?
freckles
  • freckles
oh yep you can apply the same information I just gave to that one you have period is 2pi 2pi=2pi/|b| means |b|=1 which means b=-1 or b=1 phase shift (think horizontal shift): solve inside=0 to get phase shift and as you see x-pi=0 gives x=pi so pi is the phase shift the vertical shift is yes the number hanging outside the d=-4
anonymous
  • anonymous
yay thank you :)

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