삼각함수 그래프의 성질 파악

문제

함수 $f(x) = A\sin(Bx+C)+D$의 그래프가 그림과 같다. 단, $A>0, B>0, 0 \le C < 2\pi$이다. 이때, $A+B+C+D$의 값은?

\begin{tikzpicture}[scale=0.8]
    \draw[->] (-0.5,0) -- (7,0) node[right] {$x$};
    \draw[->] (0,-2) -- (0,4) node[above] {$y$};

    % x-axis ticks
    \foreach \x/\label in {1/\frac{\pi}{6}, 2/\frac{5\pi}{12}, 3/\frac{2\pi}{3}, 4/\frac{11\pi}{12}, 5/\frac{7\pi}{6}, 6/\frac{17\pi}{12}}
    \draw (\x,0.1) -- (\x,-0.1) node[below] {$\label$};

    % y-axis ticks
    \foreach \y/\label in {-1/{-1}, 1/{1}, 3/{3}}
    \draw (0.1,\y) -- (-0.1,\y) node[left] {$\label$};

    % Grid lines for max/min/midline
    \draw[dashed, gray] (0,3) -- (6.5,3);
    \draw[dashed, gray] (0,1) -- (6.5,1);
    \draw[dashed, gray] (0,-1) -- (6.5,-1);

    % The function graph
    \draw[blue, thick, domain=1:6, samples=100] plot (\x, {2*sin(deg(2*(\x-1) + $ \frac{1}{3} $*pi)) + 1}); % This plot command needs adjustment for correct phase shift and x-axis mapping. Let's list the points and connect them.

    % Plotting specific points based on our derived function 2sin(2x - pi/3) + 1
    % x=pi/6 (1 unit) -> y=1
    % x=5pi/12 (2 units) -> y=3
    % x=2pi/3 (3 units) -> y=1
    % x=11pi/12 (4 units) -> y=-1
    % x=7pi/6 (5 units) -> y=1
    % x=17pi/12 (6 units) -> y=3

    \draw[blue, thick] (1,1) .. controls (1.5,2.5) and (2,3) .. (2,3) .. controls (2.5,3) and (2.5,1.5) .. (3,1) .. controls (3.5,-0.5) and (3.5,-1) .. (4,-1) .. controls (4.5,-1) and (4.5,-0.5) .. (5,1) .. controls (5.5,2.5) and (6,3) .. (6,3);

    % Mark points
    \fill (1,1) circle (1.5pt) node[above left] {};
    \fill (2,3) circle (1.5pt) node[above right] {};
    \fill (3,1) circle (1.5pt) node[below left] {};
    \fill (4,-1) circle (1.5pt) node[below right] {};
    \fill (5,1) circle (1.5pt) node[above left] {};
    \fill (6,3) circle (1.5pt) node[above right] {};

\end{tikzpicture}