Monday
December 9, 2013

# Homework Help: trigonometry

Posted by Anonymous on Monday, June 24, 2013 at 11:40pm.

Throughout the day the depth of water at the end of a pier varies with the tides. High tide occurs at 4:00 a.m with a depth of 6 meters. Low tide occurs at 10:00 a.m with a depth of 2 meters. Model the problem by using the trigonometric equation y=Acos(Bx+C)+D to show the depht of the water t hours after midnight, showing all your work..

• trigonometry - Steve, Tuesday, June 25, 2013 at 12:15am

the amplitude is (6-2)/2 = 2 So

y = 2cos(Bx+C)+D

Midway between high and low tide is (6+2)/2 = 4 so

y = 2cos(Ax+B)+4

The period is 12 hrs, so since cos(kx) has period 2π/k,

y = 2cos(π/6 x + B)+4

Since cos(x) has max at x=0, and we have max at x=4,

y = 2cos(π/6(x-4))+4
= 2cos(π/6 x - 2π/3)+4

Check:
y(4) = 2cos(0)+4 = 6
y(10) = 2cos(π)+4 = 2

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