kenneyfamily
write an equation of a sine function with amplitude 3, period 3pi/2 and phase shift pi/4
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kenneyfamily
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is it y=3sin(3x/2-pi/4)?
AERONIK
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3sin((4/3)t+(pi/4))
kenneyfamily
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what about -3sin(4x/3-pi/4)?
AERONIK
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general equation of a simple harmonic oscillator is Asin(wt). where A is the amplitude and w is the angular frequency.. amd 2pi/w is the time period...
AERONIK
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the equation you are giving should be a function of time and not distance... and by adding a minus sign you are just changing its phase by pi.
kenneyfamily
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so my answer is wrong?
kenneyfamily
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a. y = -3 sin (3x/2 - 3π/8)
b. y = 3 sin (4x/3 - π/3)
c. y = -3 sin (4x/3 - π/4)
d. y = 3 sin (3x/2 - π/4)
kenneyfamily
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those are my choices @AERONIK
AERONIK
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you got me wrong friend, your choices are definitely correct....
kenneyfamily
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wait i'm confused
zepdrix
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\[\huge y=a \sin(bx-c)+d\]\[a=amplitude\]\[\frac{2\pi}{b}=period\]\[c=phase \; shift\]
zepdrix
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Let's figure out our b term.
\[\large \frac{2\pi}{b}=\frac{3\pi}{2}\]\[\large b=\frac{4}{3}\]
I hope I calculated that correctly hehe
zepdrix
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\[\large y=3\sin\left(\frac{4}{3}x-\frac{\pi}{4}\right)\]
zepdrix
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Mmmmm I'm not sure if I did that correctly, was I suppose to factor the 4/3 into the pi/4? I forget...
kenneyfamily
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thats not an option :(
zepdrix
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Hmm
kenneyfamily
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wait yes i think so
zepdrix
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Yah I think the b is suppose to be like this...
\[\huge y=a \sin (b(x-c))+d\]
zepdrix
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Which IS one of your options, if you distribute the 4/3 to the pi/4 term.
zepdrix
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Hmm how did you arrive at your answer? :o
kenneyfamily
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i think its b. y = 3 sin (4x/3 - π/3)
zepdrix
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Hmmm I think so too :O