Graphs of the hours of daylight in certain latitudes

Question

Problem

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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.

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Request

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

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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.

Answer 1

OK, I think I got it...

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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).

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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.

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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

Answer 2

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