gaokao 2015 Q15

gaokao · China · beijing-science Trig Graphs & Exact Values
15. (This question is worth 13 points) Given the function $f ( x ) = \sqrt { 2 } \sin \frac { x } { 2 } \cos \frac { x } { 2 } - \sqrt { 2 } \sin ^ { 2 } \frac { x } { 2 }$. (I) Find the minimum positive period of $f ( x )$; (II) Find the minimum value of $f ( x )$ on the interval $[ - \pi , 0 ]$.
15. (This question is worth 13 points)\\
Given the function $f ( x ) = \sqrt { 2 } \sin \frac { x } { 2 } \cos \frac { x } { 2 } - \sqrt { 2 } \sin ^ { 2 } \frac { x } { 2 }$.\\
(I) Find the minimum positive period of $f ( x )$;\\
(II) Find the minimum value of $f ( x )$ on the interval $[ - \pi , 0 ]$.