7.
\((1)\)用辗转相除法求得\(459\)和\(357\)的最大公约数是______ .
\((2)\)已知函数\(f\left(x\right)=a\sin \left(πx+α\right)+b\cos \left(πx+β\right) \),且\(f\left(3\right)=3 \),则\(f\left(2016\right)= \) ______ .
\((3)\)抛掷一粒骰子,观察掷出的点数,设事件\(A\)为出现奇数,事件\(B\)为出现\(2\)点,已知\(P\left(A\right)= \dfrac{1}{2},P\left(B\right)= \dfrac{1}{6} \),则出现奇数点或\(2\)点的概率是______ .
\((4)O\)是面\(α \)上一定点,\(A\),\(B\),\(C\)是面\(α \)上\(∆ABC \)的三个顶点,\(∠B \),\(∠C \)分别是边\(AC\),\(AB\)的对角,以下命题正确的是____________\( (\)把你认为正确的序号全部写上\()\)
\(①\)动点\(P\)满足\(\overrightarrow{OP}= \overrightarrow{OA}+ \overrightarrow{PB}+ \overrightarrow{PC} \),则\(∆ABC \)的外心一定在满足条件的\(P\)点集合中;
\(②\)动点\(P\)满足\(\overrightarrow{OP}= \overrightarrow{OA}+λ\left( \dfrac{ \overrightarrow{AB}}{\left|AB\right|}+ \dfrac{ \overrightarrow{AC}}{\left|AC\right|}\right)\left(λ > 0\right) \),则\(∆ABC \)的内心一定在满足条件的\(P\)点集合中;
\(③\)动点\(P\)满足\(\overrightarrow{OP}= \overrightarrow{OA}+λ\left( \dfrac{ \overrightarrow{AB}}{\left|AB\right|\sin B}+ \dfrac{ \overrightarrow{AC}}{\left|AC\right|\sin C}\right)\left(λ > 0\right) \),则\(∆ABC \)的重心一定在满足条件的\(P\)点集合中;
\(④\)动点\(P\)满足\(\overrightarrow{OP}= \overrightarrow{OA}+λ\left( \dfrac{ \overrightarrow{AB}}{\left|AB\right|\cos B}+ \dfrac{ \overrightarrow{AC}}{\left|AC\right|\cos C}\right)\left(λ > 0\right) \),则\(∆ABC \)的垂心一定在满足条件的\(P\)点集合中.
\(⑤\)动点\(P\)满足\(\overrightarrow{OP}= \dfrac{ \overrightarrow{OB}+ \overrightarrow{OC}}{2}+λ\left( \dfrac{ \overrightarrow{AB}}{\left|AB\right|\cos B}+ \dfrac{ \overrightarrow{AC}}{\left|AC\right|\cos C}\right)\left(λ > 0\right) \),则\(∆ABC \)的外心一定在满足条件的\(P\)点集合中.