How to Graph Tides Using Sine Curves.

3758 Words May 11th, 2012 16 Pages

Daylight hours are dependent on sunrise and sunset times for each day which are dependent on seasonal change. The number of daylight hours can be represented by a periodic function. This periodic function can help Alaskan Council predict daylight hours for tourist travelling to watch their Bore Tide. A Bore Tide is a tidal phenomenon in which the leading edge of the incoming tide forms a wave (or waves) of water that travels up a river or narrow bay against the direction of the river or bay's current. Anchorage, Alaska is known for its famous Bore Tides. These bore tides occur at least once a day during high and low tide. Yet, health warnings are applied to viewing bore tides during low tide. Tourists have died by getting
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(Refer to Appendix 5 for the graph of the function:L=417 sin⁡[2π/365 (t-81)]+744). As a regression analysis the function itself was used to find daylight hours. The hours were then compared to the original data points. This comparison resulted in a percentage error being recorded. (Refer to Appendix 5 for the results of the function and percentage errors). The highest percentage error recorded was 7.35% on February 1st 2011. This error could be because February has 29 days in a leap year but 2011 data was used. The error could also occur because only 24 data points were used, if more data points were used a more precise graph would have been generated leaving less space for error.
Question 1e:
Simple deriving and calculus was used to verify that the equation L=417 sin⁡[2π/365 (t-81)]+744 for when the longest and shortest day of the year occur. The derivative of the function was started by using the chain rule(dy/dx=dy/du*du/dx). The derivative was found to be: dy/dx=2π/365 417 cos⁡(2π/365 t-162π/365). dy/dx was made to equal 0 therefore the equation will end up looking like: 0=cos⁡(2π/365 t-162π/365). When dealing with a cos curve on a unit circle cos can only be 0 at 90 degrees (π/2) and 270 degrees (3π/2) therefore meaning that to find the longest and shortest days (2π/365 t-162π/365) is made
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