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Answer to Question #44762 in Trigonometry for Stephanie
Question #44762
Model equation for tide: h=2 cos(π/6 t-2π/3)+4
Given the above, a large boat needs at least 4 meters of water to secure it at the end of the pier. Determine what span of time after noon, including both a starting and ending time, the boat can first safely be secured, justifying your answer.
So far, I have gotten this, but I'm stuck!
4=2 cos(π/6 t-2π/3)+4
0=2 cos(π/6 t-2π/3)
0=cos(π/6 t-2π/3)
0=cos(π/6 t) cos(2π/3)+sin(π/6 t) sin(2π/3)
Am I even remotely on the right track??? Can someone PLEASE help?!?
Given the above, a large boat needs at least 4 meters of water to secure it at the end of the pier. Determine what span of time after noon, including both a starting and ending time, the boat can first safely be secured, justifying your answer.
So far, I have gotten this, but I'm stuck!
4=2 cos(π/6 t-2π/3)+4
0=2 cos(π/6 t-2π/3)
0=cos(π/6 t-2π/3)
0=cos(π/6 t) cos(2π/3)+sin(π/6 t) sin(2π/3)
Am I even remotely on the right track??? Can someone PLEASE help?!?
Expert's answer
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Comments
I also realized that cosθ is equal to 0 at π/2 and 3π/2. Setting the argument (θ) equal to each of these will also result in 7 and 13 (or 7am and 1pm). Then knowing that tides run in 12 hour cycles, you would get the answer of 1pm and 7pm.
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