The position $\mathrm { P } ( x , y )$ of a point P moving on the coordinate plane at time $t ( 0 < t < \pi )$ is given by $$x = \sqrt { 3 } \sin t , \quad y = 2 \cos t - 5$$ At time $t = \alpha ( 0 < \alpha < \pi )$, the velocity $\vec { v }$ of point P and $\overrightarrow { \mathrm { OP } }$ are parallel. What is the value of $\cos \alpha$? (Here, O is the origin.) [4 points] (1) $\frac { 1 } { 10 }$ (2) $\frac { 1 } { 5 }$ (3) $\frac { 3 } { 10 }$ (4) $\frac { 2 } { 5 }$ (5) $\frac { 1 } { 2 }$
The position $\mathrm { P } ( x , y )$ of a point P moving on the coordinate plane at time $t ( 0 < t < \pi )$ is given by
$$x = \sqrt { 3 } \sin t , \quad y = 2 \cos t - 5$$
At time $t = \alpha ( 0 < \alpha < \pi )$, the velocity $\vec { v }$ of point P and $\overrightarrow { \mathrm { OP } }$ are parallel. What is the value of $\cos \alpha$? (Here, O is the origin.) [4 points]\\
(1) $\frac { 1 } { 10 }$\\
(2) $\frac { 1 } { 5 }$\\
(3) $\frac { 3 } { 10 }$\\
(4) $\frac { 2 } { 5 }$\\
(5) $\frac { 1 } { 2 }$