Exercise 1.1.26

Question

Sketch a rough graph of the number of hours of daylight as a function of the time of year.

Khagan Gulusoy · Accepted Answer

\begin{enumerate}
    \item[0.] From the beginning of the year, the length of daytime gradually increases. On March 21st, known as the spring equinox, the length of daytime and nighttime are approximately equal. 
    \item From March 21st to June 21st, the length of daytime continues to increase. 
    \item However, after June 21st, known as the summer solstice, the length of daytime begins to decrease.
    \item On September 22nd or 23rd, known as the autumn equinox, the length of daytime and nighttime are once again roughly equal. 
    \item From the autumn equinox until December 21st, the length of daytime gradually decreases. December 21st marks the winter solstice, after which the length of daytime begins to increase once more.
\end{enumerate}

Let $f:[0, \ 365] 	o [6.5,\ 24]$ be the function that returns the length of daytime at a given date (somewhere around southern Europe). We approximately sketch the graph of this function as follows.

\begin{figure}[H] \centering
\begin{tikzpicture}[scale=0.90]
    \begin{axis}[axis lines=left,xmin=0,xmax=365,ymin=0,ymax=24,xtick={79, 172, 266, 356},xticklabels={21.03,21.06,21.09,22.12},ytick={12},yticklabels={12h},xlabel={$t$, time of the year}, ylabel={$l$, length of daytime}]
         \addplot[domain=0:365, samples=365*10, mark=none, color=blue, ultra thick]
         {12/3* (sin(deg((x-80)/(184/pi)))+3)};

\addplot +[dashed,gray] coordinates {(79,0) (79,12)};   
         \addplot +[dashed,gray] coordinates {(172,0) (172,16)}; 
         \addplot +[dashed,gray] coordinates {(266,0) (266,12)};
         \addplot +[dashed,gray] coordinates {(356,0) (356,8)}; 
    \end{axis}
\end{tikzpicture}
\end{figure}

extit{Note: The dates must be exchanged for the southern hemisphere.}

Exercise 1.1.26

Answers

Comments

Exercise 1.1.26

Answers

Comments

Add answer