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In an Australian city the time of sunrise can be found using the trigonometric function T = 4.6 sin (e (d - 6) + 5 where Tis the number of hours past midnight and d...

Question

In an Australian city the time of sunrise can be found using the trigonometric function T = 4.6 sin (e (d - 6) + 5 where Tis the number of hours past midnight and d is the number of days into the year:

In an Australian city the time of sunrise can be found using the trigonometric function T = 4.6 sin (e (d - 6) + 5 where Tis the number of hours past midnight and d is the number of days into the year:



Answers

Daylight function for $40^{\circ} \mathrm{N}$ Verify that the function $$D(t)=2.8 \sin \left(\frac{2 \pi}{365}(t-81)\right)+12$$ has the following properties, where $t$ is measured in days and $D$ is the number of hours between sunrise and sunset. a. It has a period of 365 days. b. Its maximum and minimum values are 14.8 and $9.2,$ respectively, which occur approximately at $t=172$ and $t=355$ respectively (corresponding to the solstices). c. $D(81)=12$ and $D(264) \approx 12$ (corresponding to the equinoxes).

This question asks us to essentially determine how many hours of sunlight there on September 24th. Luckily, they doing us the information that this is the 272 167th day of the year. Therefore, we can simply plug into the equation that they've given in the original problem. And when we have won over 500 D, given the fact that D indicates the day of the year, we would plug in times to 67 You're probably gonna want need a calculator for this, as given by the fact that this involves a trick, no metric function coastline, and that's difficult to do by hand. Plugin isn't too calculator. We end up with age, which is the hours of sunlight, which gives us 1000 high as our solution to this problem.

Everyone today we're going to solve a problem about 83. Um, like I love the equals well plus 2.83 into sign toe by divided by 3 65 India do U minus 80 A. Parties. When there are 10 hours off daylight, it will be 12 plus 2.83 into sign toe, developed by 3 65 in your T minus 80 which is a cult. Okay, 2.83 into sign toe by divided by 3 65 in Duke B minus 80 equals minus two. Same by developed by 3. 65 into B minus 80 equals minus 0.7067 Don't buy. They would play 3. 65 in do do U minus 80 equals fight Bye bye. Four or minus by by four u minus 18 equals one mate to fight by eight or minus 3 65 by it you get he was There is really point. Want to fight or 34.375? It is that before today, before today, that is super very three or 308 day, which is our both full the parties when there are more than 10 hours off daylight, which is 12 plus 2.83 into side to find evidence by 3 65 into B minus eight. We just greater than that. 2.83 in Do look quite divided by flooding. 2.83 in Do Sign to buy different by 3. 65 into T minus 80. We difficult of then minus two. Sane to buy. Developed by 3. 65 into do U minus 80 is going to them minus 0.7 Little 67 He was great. Sleep three equals trees await pointed. Want to fight likeness. They're difficult. 0.3 35. The was Do thank you for this. Thank you.

Yeah, So we are giving their function. H is equal to you. Age is equal to 15 times co sign Peress cities with over 600 times D and we know TV. Put the 40 twos. Things were given that they were rated hands, which is the 42nd day off the year and we want to find a period of dysfunction. And we also want to find the value off the H given by easy what you put in you and the first we can find a period off dysfunction. And we know we know for a cause. I in function it full here. Here? Yes, basically to pie and, uh, to make one over 600 times d quoted you Hi. Which means he asked, the d A has to be 1200. Hi, and I'll be the period. So basically, when the is equal to zero assigned seriously, could you won well here and you're goes full period. And, uh, when you hit the point 1200 pie again, you come back to well again and there'll be a period and then we want to find the value of H. Basically, we talk. Remember India's equal to 40 cues. We got 40 to oversee its founder, and we have 15 design about to be 150.7. And the the answer is almost 50. So 15 ours. That's it for today. Thank you for watching US units.

So in this problem, we're looking to find how many hours of light that occur based on the equation 16 co sign one over 500 a. D. And since we're looking for the number of daylight hours on September 24 which is the 267th day of the year when I substitute 265 into my equation, they have to make sure that I'm in radiance toe work. With this, I have one over 500 times. Choose 67. I will end up getting approximately 13.77 hours using my calculator in order state the period of this function. We have to remember that the period is equal to two pi divided by the frequency. In this particular case, the frequency here is one over 500. So we have P is equal to two pi divided by one over 500 which is the same as two pi times 500 which will end up being, um uh, 1000 huh? So if I approximate that, that will be approximately 3141.6. That would be our period


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