Today in class we went over a new type of problem about Trigonometric Modeling and Transformations. The problem is my computer won't allow me to download any of the slides so I have to explain the process to the best of my ability without using any of the slides as reference.

In class we learned how to apply the stuff we have been learning to more real life situations. For part (a) in the example. We started by labelling the x-axis values starting with 0= December 31, -10=December 21 and 172= June 21 because June 21 is the 172nd day in the year and so on for the rest of the values. Then we labeled the y-axis with the values necessary 9:15=9 + 15/60 or 1/4. and 3:15=3.25. The sinusoidal axis being exactly half way in between 9.25 and 3.25 which is 6.25. Then we are told that on Dec 21 its at 9.25 and at June 21 its at 3.25 and then we just connected the dots and completed the graph.

For part (b) we found the equations from the graph, A= the amplitude which is 3 which can be seen from the distance from the sinusoidal axis to the min or max. Then we found the period by again just looking at the graph and the information already given and because the distance between Dec 21 and June 21 is half a period and 182 days then a full period is 364 days. So B=2(pi)/364. C and D are found the way they are normally found.

For part (c) it is simply done by finding what day # April 6 which is day 96 and then substituting 96 every place where the variable "d" is found and then solving for it.

Part (d) asks for the average which is just the value of the sinusoidal axis which is 6:15am.

In part (e) you must put 7:00am into the outputs and then do the equation into reverse and find out what dates the sun rises at that time. To simplify this equation we substituted the values inside the square brackets for theta and then found the two possible values for theta which gave us our two answers.

Now sorry fellow classmates for having this being so complicated and not having the proper diagrams to actually explain but I attempted to do it to my best ability and tried to explain it to the best of my understanding and I hope this is at least a little helpful to anyone planning on using this to help them but I'm not exactly sure it will. Sorry.

The next scribe is Bryan L.

And Alvin for next time its SERGIO.

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## 1 comment:

Because of the fact that Sergio did not give up after finding that he could not download the slides (which at certain times, I might've), I vote this scribe post be put into the Hall of Fame. &because of how well he explained something that we JUST got introduced to, even without the help of slides to help his explaination. &thnx Serg... I knew I'd have to be scribe next!.. HAHA

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