Salam, can you please answer this? And I don't even know what an equinox is (used in the question) and wikipedia has a lot of information that is neither understandable nor do I have the time to read...

Q: At a certain latitude in the northern hemisphere, the number 'd' of hours of daylight in each day of the year is taken to be d=A+Bsinkt (degrees), where A, B, k are positive constants and t is the time in days after the spring equinox.

a)Assuming that the number of hours of daylight follows an annual cycle of 365 days, find the value of k, giving your answer correct to 3 decimal places.

b) Given also that the shortest and longest days have 6 and 18 hours of daylight respectively, state the values of A and B. Find, in hours and minutes, the amount of daylight on New Year's Day which is 80 days before the spring equinox.

c) A town at this latitude holds a fair twice a year on those days having exactly 10 hours of daylight. Find, in relation to the spring equinox, which two days these are.

(from A Level Pure Maths 1 by Hugh Neil and Douglas Quadling)

Simply give you the answer? Not going to happen. The responsibility for the time and effort to learn your own homework is on you.

This problem is a specific application of using a sinusoidal equation to model some real-world situation.

The general idea is that by adjusting the variables A, B, k, and t appropriately, you are adjusting the basic sine wave (stretching or shrinking vertically, compressing or expanding horizontally, shifting left / right / up / down) such that the resulting altered sine wave fits your real-world phenomenon.

Starting with a basic sine curve, think of those variables as "tuning knobs", with each one having a specific morphing effect on the curve. In your case you want to "tune" those variables in such a way that the resulting sine function runs one cycle over a 365-day period, and with the height of the curve giving the number of daylight hours on each such day.

Take the time to learn about sinusoidal functions in general, and the payoff will be that you'll become pretty adept at using 'em to model just about any real-world phenomena involving cyclical behavior.

Just to add - you really don't need to worry about what the spring equinox is - just think of it as the time when the sine sin(kt) function crosses the 't' axis, going from negative to positive values. On that date every place on the earth has exactly 12 hours of daylight and 12 hours of night (oops, I just gave you the answer for 'A').

Umm... thanks. But you see I always try a question myself before asking. Point is I know what you are talking about the sine wave, plus I have done the whole chapter. This particular question was confusing. Cux of the language e.g.. I didn't know what was being asked... and other reasons. Moreover, when someone asks you for help, you just have to give it. I am responsible enough to not ask for it unless I need it. Did you know: being taught is one of the ways people learn? U just had to lecture me... on the question you see..

Just to add... this is not what I joined your site for! U go to a tutor so that he can teach you not so that he tells you to run off and figure things out for yourself! By the by I am done here!

And o yes... I forgot to mention, please change the name of your site from 'ask me help' to 'ask me help so that I can tell you to find it yourself'. I know it's long but at least not false promotion!

How are you exempt from this forum's homework help rules (IN RED) which you undoubtedly read, being the responsible chap you are? What did those rules say, and how are you exempt?


umm...thanks. but u see i always try a question myself before asking. point is i know what u are talking about the sine wave, plus i have done the whole chapter.

My bad. All I saw in your first post was that you tried to find the answer on Wiki, but didn't have time to read it. I missed where you explained that you had already made a valid effort at answering this question, and showed your attempt. Here's your chance to embarrass me by pointing all this stuff out in your first post. I'll wait.


moreover, when someone asks u for help, u just have to give it.

Wrong. Your sense of entitlement will surely serve you well in the real world.

Wake up. Look at the other posts around this forum. The questions from folks who take the personal responsibility to show some serious effort receive plenty of tips, guidance, hints, and advice, from the people who freely and generously volunteer their time here. Those who want to offload their homework responsibilities onto someone else and be spoon-fed the answers get ignored.

The former ends up learning a lot; the latter learns nothing. Pick your group.

Make the right choice, and you'll end up doing well, amigo.