Graphs of the hours of daylight in certain latitudes Problem


Attempt
We are given that Graph A is North.
Since South is more "dark" when North more "light" I picked the graph that is mirrored horizontally: Graph D.
For East and West I can only guess.


Request
  
  
*
  
*Clarify my logic for Graph D corresponding to South.
  
*Explain what Graphs B and C correspond to.
  


Disclaimers


*

*This may need problem may require some astrophysics trivia, but this problem was found in "Trigonometry" by I. M. Gelfand, a (surprise!) trigonometry textbook.

*I understand that it is preferred that I type the problem out rather than take a picture of the page, however I was not willing to spend time recreating the graphs.
 A: OK, I think I got it...

Prerequisites


*

*I will be calling the graphs by letters A-D. (i.e. A corresponds to Graph A).

*I will be calling the cardinal directions N, E, S, W. (i.e. N corresponds to north).

Solution
A is given to be N.
D is A flipped horizontally. It is fairly obvious that D is S.
The rest of the solution is where I was stumbling. However, the title actually may have given me a hint. I had assumed that B and C must be in E and W, but I wasn't sure which one corresponded to which. Note that the title says "latitude". This hinted me that the only 2 hemispheres we could possible be talking about is N and S.
B and C are both A stretched vertically. They ought still be N. We can be a bit more specific, though. It's more-less common knowledge that the amount of daylight in the poles oscillates much more extremely (i.e. larger amplitude). So we can say that C is more N than A and B is more S (but still N) than A.

Answer


*

*A is N

*B is N (least N of A, B, C)

*C is N (most N of A, B, C)

*D is S

A: From geography, we know that 
Variation in daylight time:


*

*at equator, and latitudes near equator, is minimum. The daytime is approximately constant throughout the year. So most likely, none of the graphs correspond to this.

*is maximum near poles, so most likely, plot C corresponds to a place near arctic circle (not near antarctic circle, since graph C is similar to graph A, which is lying in north hemisphere.)

*is very less in the latitudes lying between Tropic of Cancer and Tropic of Capricorn. So, it is likely that plot B is of a latitude near to Tropic of Cancer (not tropic of Capricorn, by the same argument as the last point.)

*in plot A is greater than in plot B, but less than that in C. So i think this plot is of a latitude between Tropic of Cancer and Arctic Circle. Also, as you figured out, plot D corresponds to a region as much south of equator as region A is north of it. So, plot D should correspond to a region between Tropic of Capricorn and Antarctic Circle.
Read more about Daylight Variation here: Daytime - Wikipedia
