#sinusoidal graph word problem

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tacit axle
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Need help on this question, I got it wrong on my exam review booklet. help me how to get to answer key answer of 6.4

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golden cave
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and midline i guess

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get those out of the way

tacit axle
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amplitude is 2.5, midline is at 8.3, period i have 2pi/9

golden cave
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and the x axis is x hours after midnight righit

tacit axle
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yes

golden cave
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the period isnt 9 in that case

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when does it hit max again

tacit axle
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what will the period be

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it is at max at 10.8 at midnight

golden cave
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but when is it max again

tacit axle
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i dont know, sorry

golden cave
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okay, uhhh

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a wave goes from max to min back to max

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and these two times are equal right

tacit axle
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yes

golden cave
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the time it takes to go from max to min is the same as it takes to go from min to max

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so with that in mind

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can you find the period

tacit axle
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im still thinking its 9

golden cave
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period is the time it takes to reach the same place on the graph

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so max to min is 9 hours

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thats not the same

tacit axle
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24?

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cause the full day

golden cave
tacit axle
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9

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period is 18

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im really lost

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sorry

golden cave
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yup

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so now whats the like

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coeficient for the uh

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sin/cos(ax)

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the a

tacit axle
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2pi/18 so reduced it is pi/9

golden cave
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yup

tacit axle
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i believe there is no phase shift

golden cave
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yup

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but which function do we use

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sin or cos

tacit axle
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sin

golden cave
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remember we start at a maximum

tacit axle
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the word problem says its sinusoidal

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although i made it cosine anyways and got the correct answer

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how can i do this question in sin?

golden cave
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you’d need a shift

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just don’t

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cos is much easier