## Wednesday, March 12, 2008

### Yet Another Workshop Class

Hello once again, it is I, Kristina, back for another scribe post. Today, we were supposed to have a pre-test in the morning and the actual test in the afternoon but we ended up only having the pre-test in the afternoon. The reason why was because Mr. K thought that we weren't ready to have the test after seeing us somewhat struggle over yesterday's class. So, in the end, we ended up using the morning class to have a workshop period! Yay, fun..

After we had been split into our groups, which there were a t
otal of four, we were given a question to work with. I will type out the question, which is already on slide 2, for your convenience.

At a sea port, the depth of the water, h meters, at time, t hours, during a certain day is given this formula:

A) State the: i) period ii) amplitude iii) phase shift

This was the first part of the question, which should be fairly straight forward. BUT! It ended up not being so straight forward to the class. Every group came to the same conclusion for the amplitude and phase shift, but the class became divided with finding the period. Which is shown in slide 2 with the two different answers.

The first answer (red) is not the right answer, the one in blue is the correct one. This is because the group who put up answer red didn't factor out parameter B correctly. They thought that because since 2pi wasn't "visually" over 12.4, that they had to factor that out first
and then multiply 2pi by 12.4 to isolate parameter C. After a bit of arguing and confusion, Mr. K kindly showed us that even though the 2pi didn't appear to be over 12.4, it actually was. The reason for this is because that 2pi could also be seen as 2pi/1, which, when multiplied, actually gives 2pi(t-4.00)/12.4! Now, from there all you need to do to get the period is to factor out the 2pi/12.4 to get parameter B and then to get divide that from 2pi. Voila, you should then get the answer of 12.4. We can then move onto the next question..

B) What is the maximum depth of the water? When does it occur?

Now, for this part of the question, I am going to explain how to do it in a completely different way from what the slide shows you. The reason for this is because, in my own opinion, it doesn't depict a very accurate and understandable way on how to find the actual value. By just using the graph to try and find it, I think its just like guessing, therefore not very accurate. The graph is only good when you want to pinpoint which areas the answer will be in, which is actually shown very nicely on the graph in slide 4.

Well then, to show how to get 7.1 hrs as the answer, I am going to show you how to get it MATHEMATICALLY using the formula!

Looks difficult? Nah! Its so simple! You see, all I did was input the max value, which was 4.9 into h(t) . From there, I then solved for t. I'm sure most of you have gotten stuck after getting to the ARCsin part, well then don't fret, because I've also had troubles with that in the past. All you have to do to isolate the (t-4) is to multiply both sides by the reciprocal of 12.4/2pi. When you do this, 2pi/12.4 on the right side will get cancelled out and then you will be left with 12.4/2pi * ARCsin(1) = t - 4. From there's its baby stuff! We're all in pre cal, I don't think you need me to explain what to do from there. Anyways, I hope this solves any problems people had with slide 4. MOVING ON..

C) Determine the depth of water at 5:00 A.M. and at 12:00 noon.

This is simple, all you have to do is input 5 and 12 into the value for t and then solve from there. If you need further explanation for this, feel free to add a comment since I am seriously getting tired right now haha >_<.

D) Determine one time when the water is 2.25 meters deep.

Okay, this is basically the same as letter B. Instead of 4.9, input 2.25. Then solve from there. No further explanations need to be said for how to do these kind of questions. But, in case you do, please leave a comment!

AWWRIIIGHT! Moving onto the afternoon class! First thing we did was have a PRE-TEST! We were given about, I don't know, 20 minutes? to do it and then we were put back into the same groups we were in for the morning class to discuss our answers so that we could hand it in, but only one person's pre-test was handed in.

We then went over the answers after having handed in one person's pre-test. The multiple choice answers were pretty straightforward, so I am going to skip to the very last question since it was definitely the hardest one out of them all.

Starting off with the question "a)" of the last question. Its asked to sketch a graph of the height of the point A above the outflow water level as a function of time starting at t = 0 seconds, with A as shown in the diagram. The first thing you had to do to be able to graph this was to find the period. We were able to get the period from the information in the question that said there were 5 revolutions every 4 minutes. From this info, we can then find the period by attempting to when 1 revolution occurs, which will end up in seconds. As slide 12 shows, the period will be 48 seconds since that is when 1 revolution occurs. The graph can now be made easily and the reason why it starts at 0 is because starting at 0 seconds, point A is still above the outflow.

Part "b)" of the question is pretty self explanatory. All you had to do was take a look at the graph and then find the different parameters for SINE and COSINE. From there, you would be able to get the same answers as shown in the slide if you did it right. As for part "c)", this is just like question "B" from the morning class. Instead, you can choose between which formula you want to work with, either the SINE or the COSINE that you made in the previous question. Once you've done that, just input 4 into h(t) and then solve for "t" in the exact same way as shown in "B" from the morning's question. After having solved for question "c)", you can now solve for question "d)". Take a quick look back at the graph and find where 4 meters would be. If you draw a straight line across, you'd see that it touches two parts of the wave. That is why the answer shows that you have to multiply the answer by 2.

After we had finished going over all the answers, Mr. K then told us that we had a group assignment to do. Each group was given an assignment that was similar to the questions we had done today. They're expected to be posted onto the blog with the appropriate tags: "TrigAssignment, (names of group members), Transformation. The due date is on MARCH 13 BY NOON. Once every group has got their assignment posted, everyone is expected to comment on each of the groups' assignments, excluding their own, whether they be about how neat their work was, or if they found an error, etc.

Now then, I guess that's all for me. REMEMBER GUYS! TOMORROW'S PI DAY! Make sure you don't forget to bring your delicious pies! As for the lucky scribe for Pi Day, I choose....Roxanne. Well then, that's all for me. Oh yeah, and remember! THE TRANSFORMATIONS TEST IS ON FRIDAY AFTERNOON! For those of you who haven't BOB'd yet, be sure to do it by then! Alrighty, now seriously, I'm out.