In the coordinate plane, point A has coordinates $( 1,0 )$, and for $\theta$ with $0 < \theta < \frac { \pi } { 2 }$, point B has coordinates $( \cos \theta , \sin \theta )$. For point C in the first quadrant such that quadrilateral OACB is a parallelogram, let $f ( \theta )$ be the area of quadrilateral OACB and $g ( \theta )$ be the square of the length of segment OC. What is the maximum value of $f ( \theta ) + g ( \theta )$? (Here, O is the origin.) [4 points] (1) $2 + \sqrt { 5 }$ (2) $2 + \sqrt { 6 }$ (3) $2 + \sqrt { 7 }$ (4) $2 + 2 \sqrt { 2 }$ (5) 5
In the coordinate plane, point A has coordinates $( 1,0 )$, and for $\theta$ with $0 < \theta < \frac { \pi } { 2 }$, point B has coordinates $( \cos \theta , \sin \theta )$. For point C in the first quadrant such that quadrilateral OACB is a parallelogram, let $f ( \theta )$ be the area of quadrilateral OACB and $g ( \theta )$ be the square of the length of segment OC. What is the maximum value of $f ( \theta ) + g ( \theta )$? (Here, O is the origin.) [4 points]\\
(1) $2 + \sqrt { 5 }$\\
(2) $2 + \sqrt { 6 }$\\
(3) $2 + \sqrt { 7 }$\\
(4) $2 + 2 \sqrt { 2 }$\\
(5) 5