Question 847223: Hi, I am stuck on this question because I am not sure what function and what range I am superposed to use. I am also not sure how to set up this question. Any help is appreciated. Thank you!
i) Graph a trigonometric function that maps the level of the sea in a harbor throughout a day; if we begin measuring at 00;00 midnight and it is at high tide of 7m.If the lowest it reaches is 2m and two full revolutions of the tide occur in 24hours.
ii) At what times of day is the tide at 6m in height, closest to the nearest meter.
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! since high tide occurs at midnight, I will use the cosine function
the general form of cosine function is y = a * cosbx + c, where * means multiply
a is amplitude = max - min / 2 = 7 - 2 / 2 = 2.5
b is period = 360 / |b| = 12 and b = 30
c is prin axis = max + min / 2 = 7+2 / 2 = 4.5
therefore the equation is
y = 2.5 * cos 30x + 4.5 = (5*cos 30x + 9) / 2
x axis is 0 to 24 and y axis is 2 to 8
a tide of 6m occurs at 2am, 10am, 2pm, 10pm
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