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 March 13th, 2014, 02:21 PM #1 Senior Member   Joined: Apr 2008 Posts: 194 Thanks: 3 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.
 March 13th, 2014, 05:38 PM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,950 Thanks: 1141 Math Focus: Elementary mathematics and beyond Re: What did I do wrong? Are you told what depth of water the ship needs to dock safely?
 March 14th, 2014, 03:34 PM #3 Global Moderator   Joined: May 2007 Posts: 6,785 Thanks: 707 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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