8.
\((1)\)已知向量\(a\)\(=(2,—1)\),向量\(b\)\(=(\)\(m\),\(3)\),若\(a\)\(/\!/\)\(b\),则\(m\)的值是_______。
\((2)\)已知
\(\tan \)\(α=3\),则
\(\sin \)\(α\)
\(\sin \)\((\)
\( \dfrac{3π}{2} \) \(-α)\)的值是 ______.
\((3)\)下列说法:
\(①\)正切函数
\(y\)\(=\)
\(\tan x\)在定义域内是增函数;
\(②\)函数
\(f(x)=\cos ( \dfrac{2}{3}x+ \dfrac{π}{2}) \) 是奇函数;
\(③\)
\(x= \dfrac{π}{8} \) 是函数
\(f(x)=\sin (2x+ \dfrac{5π}{4}) \) 的一条对称轴方程;
\(④\)扇形的周长为\(8\)
\(cm\),面积为\(4\)
\(cm\)\({\,\!}^{2}\),则扇形的圆心角为\(2\)
\(rad\);
\(⑤\)若\(α\)是第三象限角,则
\( \dfrac{|\sin \dfrac{α}{2}|}{\sin \dfrac{α}{2}}+ \dfrac{|\cos \dfrac{α}{2}|}{\cos \dfrac{α}{2}} \) 取值的集合为\(\{-2,0\}\),
其中正确的是 ______\(.(\)写出所有正确答案的序号\()\)
\((4)\)
\(a\),
\(b\),
\(c\)分别是\(\triangle ABC\)内角\(A\),\(B\),\(C\)的对边,
\(a\)\(+\)
\(c\)\(=4\),
\(\sin \)\(A(1+ \)
\(\cos \)\(B)=(2-\)
\(\cos \)\(A)\)
\(\sin \)\(B\),则\(\triangle ABC\)面积的最大值为 ______.