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March 13th, 2014, 02:21 PM   #1
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What did I do wrong?

By using the averages of high and low tide levels, the depth of water can by approximated by d(t) = 2.5 sin(0.164*pi*(t-1.5)) + 13.4. A cruise ship needs a water depth of least 12 meters to dock safely. For how many hours per tide cycle, can the ship dock safely?

My attempt

12 = 2.5 sin(0.164*pi*(t-1.5)+13.4

reference angle t = 0.594

so, I put this reference angle in quadrants 3 and 4 where the ratio of sine is negative.

Then, the standard position angles in 3 and 4 are 8.75 and 12.54 respectively.

Hence, 12.54 - 8.75 = 3.79.

But, this is wrong. Could someone please explain it? Thanks.
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March 13th, 2014, 05:38 PM   #2
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Re: What did I do wrong?

Are you told what depth of water the ship needs to dock safely?
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March 14th, 2014, 03:34 PM   #3
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Re: What did I do wrong?

The ship can certainly dock safely when the sine is in the first two quadrants. Therefore you should have more than half a day. You need to exclude the range of t where sin < -.56.
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