已知向量\( \overrightarrow{a}=\left(3,1\right) \)，\( \overrightarrow{b}=\left(-2,4\right) \)，求\( \overrightarrow{a} \)在\( \overrightarrow{b} \)方向上的投影为         ．

\((1)\)已知向量\(\overset{}{a}\)，\(\overset{}{b}\)，若\(\overset{}{a}\)在\(\overset{}{b}\)方向上的投影为\(3\)，\(\left| \overset{}{b} \right|{=}2\)，则\(\overrightarrow{a}\cdot \overrightarrow{b}=\)__________．

\((2)\)若函数\(f(x)=\sin \pi x,x\in [\dfrac{1}{3},\dfrac{5}{6}]\)，则\(f(x)\)的值域为___________．

\((3)\)已知\(\cos (\dfrac{\pi }{6}-\alpha )=\dfrac{2}{3}\)，则\(\sin (\alpha -\dfrac{2\pi }{3})=\)__________．

\((4)\)若函数\(f(x)=\dfrac{2{{(x+1)}^{2}}+\sin x}{{{x}^{2}}+1}\)的最大值和最小值分别为\(M\)、\(m\)，则函数\(M+m=\)_______．

已知\(|a|=1\)，\(|b|=2\)，\(a\)与\(b\)的夹角为\(60^{\circ}\)，则\(a+b\)在\(a\)上的投影为________．

\((1)\)化简\((\overrightarrow{AB}-\overrightarrow{CD})+(\overrightarrow{BE}-\overrightarrow{DE})\)______ ．

\((2)\)若\(\overrightarrow{a}{=}(2{,}3){,}\overrightarrow{b}{=}({-}4{,}7)\)，则\(\overrightarrow{a}\)在\(\overrightarrow{b}\)上的投影为__   ____ 。

\((3)\)已知\(\sin 110^{{∘}}{=}a\)，则\(\cos 20^{{∘}}\)等于__________。

\((1)\) \(\sin \)\(11^{\circ}\)\(\cos \)\(19^{\circ}+\)\(\cos \)\(11^{\circ}\)\(\sin \)\(19^{\circ}\)的值是 ______．

\((2)\)函数\(f\)\((\)\(x\)\()=3\)\(\cos \)\(( \dfrac{π}{2} \)\(x\)\(- \dfrac{π}{8} )\)的最小正周期为 ______．

\((3)\)已知角\(α\)终边上一点\(P(-12,5)\)，则\(\cos \)\(α= \)______．

\((4)\)已知向量\( \overset{→}{a} \)与\( \overset{→}{b} \)的夹角为\( \dfrac{2π}{3} \)，\(| \overset{→}{a}|= \sqrt{2} \)，则\( \overset{→}{a} \)在\( \overset{→}{b} \)方向上的投影为 ______．

\((5)\)若\(\tan \)\(α\)，\(\tan \)\(β\)是方程\(x\)\({\,\!}^{2}-3 \sqrt{3} \)\(x\)\(+4=0\)的两个根，则\(\tan \)\((α+β)= \)______．