Um So this question, we're looking at a phase shift and Sino Soto curve fittings. Right? Um, so the information we're given in the beginning of the problem is that the time. But we in two consecutive high tides is going to be 12 hours and 25 minutes. Right, So 12 hours and I've been to 25 minutes. Right? And according to National Oceanic and everything, uh, Saturday, April 26 2014, that's all. Uh, not that important information. High tide has occurred at 6:30 a.m. 6. 30 a. M. And that was a high tide. Right? So we know that now, at 12. 24 p. M. We've got a low tide. So we have that information as well, and then we also have information of water heights. Right. So the height of the water at high tide was 5.86 ft, and the height at low tide was negative. 0.38 ft. Yeah. And the question they're asking is, uh, when will the next high tide occur? So that is the first question. When will the next high tide occurred? Well, we know that the high tide occurs every 12 hours and 25 minutes. And we know that the first high tide occurred at 6:30 a.m. So if you take 6:30 a.m. and you add 12 hours and 25 minutes to it, Yeah, then what do you get? Well, uh, 12 hours past 6:30 a.m. will be 6. 30 PM right? So that they get rid of the 12 hours and then you simply add 25 minutes and then you'll get 6:55 p.m. So 12 hours and 27 minutes, 25 minutes after the first high tide, it will be 6. 55 PM So this is when the next high tide will occur, right? So that would be your answer for part one. And then we'll go to part two or part B. And this part is asking us to find the function in the form of Y equals a sign of Uh huh w X minus five. Our road. Uh, this is another Greek symbol, plus B, right. So we need to find a function in this form, and in order to do that, you have to know that first, eh is going to be equal to the maximum. One is the minimum over to. Right. So this is gonna be the max, which is 5.886 ft, um, minus the minimum, which is 0.38 ft. I sorry. Negative. 0.38 ft. And I divide those two by two. To get a and then to get B B is actually going to be the maximum minus a. Now you be and then to get omega or W That's an Omega. And you have to do to pi over, um, over P, which is the amount of time it takes because that you're going from one high tide to another high types from one peak to another people. So how long does it take to complete one full cycle? That's what P is. And what else do you know? Well, that's pretty much it right. Um, and I guess the other thing you need to know is that, um is your is your charge? The other thing you need to know is is your is your angle here or your value here, And that value will just simply be, um what? Your first? When was your first um, when was your first thing? Your first high tide. And that was at 6. 55 PM or sorry. 6:30 p.m. So that will be equal to 6.5. Right? So, yeah. So, um, this dis variable here is going to be how much it shifts by, um, which is basically where the when the first high tide came in. And the first high tide, of course, came in at 6. 30 AM I right? So 6.5 will be the shift there. Um, so when you plug everything in, you should get y equals A which is going to be maximum time is the minimum, and that's going to be Let's see, that was going to be a 5.86 minus negative. 0.38 Yeah. Uh, it's gonna be 6.2 4/2. It's gonna be 3.12 Time signed of Uh huh. So, yes, I sign times two pi over and R P is going to be the total time it takes, which is 12 hours and 25 minutes. Uh, 12 hours and 25 minutes is actually gonna be 12.42 um, 12.42 Right. And then all of these times x minus. Um, yeah, uh, 6.5. Right. And plus maximum, which is 586 minus eight, which is 3.12 And you get 2.74 So that's going to be basically your equation. And you can simplify that down to, like those three, uh, 3.12 times sine of two pi over 12 or 42 X minus 17184 plus 274 So that is going to be the form that your answer is going to be in mhm. All right. Okay. Okay. So, um Right, so now that you have that, uh, what you gotta do next is part seat, uh, which is actually asking us, Um uh, approximately using the function that we just made, uh, find the height of the water at 3 p.m. So 3 p.m. is going to be We can't just plug that straight into our equation here because we have to convert 3 p.m. Into military time. So three PM is actually gonna be 15, um, in military time, because you take 12 and then you add three and you get 15. 12 will be the maximum at at noon, and then you add three. Because you're going past noon to 3 p.m. And then you get 15. So then, now that we have that, we basically just want to plug in. Why? 15? And when we do that, we'll get 3.12 times sine of two pi over 12.42 Um, Times 15 minus 17184 plus 2.74 So we do that when we take the sign. Right? So to pi over 12.42 Um, that will be zero, uh, to pi over 142 there'll be mhm. Um um All right. Right. So, uh, to pi over 12.42 is 0.506 and then you multiply that by 15, and then you subtract one point 7184 get you 5.87 and you take the sign of that. Uh, you get 0.10 So you have, um, 3.12 times 0.102 and then you add 2.74 And then when you multiply by 3.12 and then add 2.74 Yeah. Um, yeah. Um Oops. Sorry. Sign of sign of 5.87 is not that sign of 5.87 is actually, uh, negative 0.399 don't forget to switch your calculator into radiant mode because we're dealing with radiance now, not degrees. Um, And then you should also get the same answer as I did here, So yeah. 0.399 And then you take that. You multiply by 3.12 you get negative 1.24 and you add that to 2.74 and then you get 1.4931 point 493 ft. So that will be your approximate answer for your height. So your height at, um, at a time, yeah, R 3 p.m. will be approximately equal to 1.493 So that will be your final answer for that one as well. So now you have the answers to all of them. Um, so, yeah, in general. So the first part was really easy. We just have to, uh, do some addition there with time. Second part. I was slightly harder. Just remember all these techniques here, um, for finding all these calculating all these things and calculating all the phase shifts, um, and fitting things into your Sinus over the old function, and then down here was just plugging in. So overall, pretty simple. Um, so that's it.