已知函数\(f(x)=\begin{cases} & \log \dfrac{1}{2}x,x > 0, \\ & \cos x,x\leqslant 0, \end{cases}\)则\(f\left( f\left( -\dfrac{\pi }{3} \right) \right)=\)________

设定义在\(R\)上的奇函数\(y=f(x)\)，满足对任意\(t∈R\)都有\(f(t)=f(1-t)\)，且当\(x∈[0,\dfrac{1}{2}]\)时，\(f(x)=-x^{2}\)，则\(f(3)+f\left( \mathrm{{-}}\dfrac{3}{2} \right)\)的值等于 \((\)　　\()\)

已知在\((0,+∞)\)上函数\(f(x)=\begin{cases} -2,0 < x < 1 \\ 1,x\geqslant 1 \end{cases}\)，则不等式\(\log _{2}x-(\log _{ \frac{1}{4}}4x-1)·f(\log _{3}x+1)\leqslant 5\)的解集为\((\)　　\()\)

\((1)①\dfrac{2\sin {{46}^{\circ }}-\sqrt{3}\cos {{74}^{\circ }}}{\cos {{16}^{\circ }}}=\) _________    \(\_\)．

\(②\sin 42{}^\circ \cos 18{}^\circ -\cos 138{}^\circ \cos 72{}^\circ =\)________    __．

\((2)①\)设函数\(f(x)=\begin{cases} & x,x < 1 \\ & {{x}^{3}}-\dfrac{1}{x}+1,x\geqslant 1 \\ \end{cases}\)，则不等式\(f(6-{{x}^{2}}) > f\left( x \right)\)的解集为____       \(\_\)

\(②\)设函数\(f(x)=\begin{cases} & x,x < 1 \\ & {{x}^{3}}-\dfrac{1}{x}+1,x\geqslant 1 \\ \end{cases}\)，则\(f(\dfrac{1}{f(2)}) =\)__________

\((3)①\)将函数\(f(x)=\sin (3x+ \dfrac{π}{4}) \)图像向左平移\(m(m > 0)\)个单位后所对应的函数是偶函数，则\(m\)的最小值是             ．

\(②\)函数\(f(x)=\sin (3x+ \dfrac{π}{4}) \)的最小正周期为              ．

\((4)①\)等腰\(\Delta ABC\)的顶角\(A=\dfrac{2\pi }{3}\)，\(\left| BC \right|=2\sqrt{3}\)，以\(A\)为圆心，\(1\)为半径作圆，\(PQ\)为直径，则\(\overrightarrow{BP}\cdot \overrightarrow{CQ}\)的最大值为\(\_\)___   ______．

\(②\)等腰\(\Delta ABC\)的顶角\(A=\dfrac{2\pi }{3}\)，\(\left| BC \right|=2\sqrt{3}\)，则\(\overrightarrow{BA}\bullet \overrightarrow{AC}=\)_____    _____．