Tide Problem

[csikes]

I searched the threads and I know variations of this problem is out there, but I had a question about my work. Here is my work...



SO..... My mistake is my C value. I think taking the inverse of cosine is messing me up. I'm thinking I am going to have to focus on the B value to help me, but I can't figure out how to make the B value help me. Can anyone give me any suggestions?

 

[mmm4444bot]

Why do you think that C = -Pi/3 is incorrect?

Another way of looking at the following:

cos(Pi/3 + C) = 1

We already know that cos(0) = 1.

Hence, Pi/3 + C = 0, and C = -Pi/3.

I think that's easier than using the inverse.

 

[wjm11]

I searched the threads and I know variations of this problem is out there, but I had a question about my work. Here is my work...
View attachment 2145

View attachment 2142View attachment 2143
SO..... My mistake is my C value. I think taking the inverse of cosine is messing me up. I'm thinking I am going to have to focus on the B value to help me, but I can't figure out how to make the B value help me. Can anyone give me any suggestions?

Concerning the period of the function: There are two high tides each day, not one, so the period is approximately 12 hours (closer to 12 hours, 25 minutes actually). So B = 2pi/12 = pi/6. You'll need to recalculate C based on this, but your approach looks fine.

 

[csikes]

Hmm, I know that my c-value should be pi/6, but the question is how to get there. I like the idea of the tide being only 12 hours, but the reason why I haven't tried changing others is because the evaluator who looked over this said:

The A, B, and D values of the trig equation are accurately found within the submission, however the C value is not stated correctly.

So, the question is, how do I get pi/6 (a mentor said that C should be this, but she gave this as a means to help me figure out how to get that... it didn't help, lol) for my C value without changing my B value?

Oh, and here was the original problem... sigh... I forgot I didn't put it in.

y = A cos(Bx + C) + D. Tides vary throughout the day. High tide occurs at 4:00 a.m. with a depth of 6 meters. Low tide occurs at 10:00 a.m. with a depth of 2 meters. Model a function based on this information. Then find the depth of the tide at noon and then list the times when the tide is at least 4 meters.

 

[csikes]

Whether we should give any weight to your preferences about the period of the tides and regardless of the empirical facts, the problem indicates that you are to use a period of TWELVE hours, not twenty-four. Low tide at 4 am. High tide at 10 am. 6 hours from trough to crest implies a complete tidal cycle of 12 hours.

I understand that it should be 12 hours, but my issue is that when I submitted the document to the evaluator, they said that only my C value was incorrect. This implies that B is fine, based on 24 hours. Well, maybe the evaluator is wrong... -_- which means I've spent days on this problem when I could have easily fixed my B value and corrected C based on that. Thanks for the help you guys! I am going to email my mentor to see if there is a way to double check what the evaluator wrote is true or not. If I can change my B value, then it will all work out like the first correction I made.