How to solve a trigonometry wave height problem
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How to solve a trigonometry wave height problem

[From: ] [author: ] [Date: 11-07-08] [Hit: ]
So the biggest wave is 3.4*1+3.8.The sine wave is the height of the waves that oscillates between +3.4 and -3.4 on top of the mean sea level 3.......
A data buoy measures wave height and transmits the info to a monitoring station. For the minute 11:11 (high tide), wave height can be modeled with the equation y = 3.4 sin ( 2pi/10t) + 3.8 where t is measured in seconds y is in feet. Determine max height of a wave above clam sea and how many waves break during this minute.

I have no idea how to approach this

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Some pointers

The maximum of sin(anything) = 1

So the biggest wave is 3.4*1+3.8.

The sine wave is the height of the waves that oscillates between +3.4 and -3.4 on top of the mean sea level 3.8.

So the biggest wave is 3.4m

The equation of an oscillation, or a wave is sin(2*pi*f*t) where f is the frequency

Alternatively it is sin (2*pi*t/T) where T is the period.

Looking at the equation above, f = 1/10 or T = 10, so the frequency is 0.1Hz and the period is 10sec. The period is the time between successive waves.

If it's 10sec between waves then there are 6 waves in a minute. Or if there's one wave breaking at t=0 then there'll be 7 waves, because the 7th will break when t=60.
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