知识点挑题 - 高中数学 - 优优班--学霸训练营

1．
\(\Delta ABC\)的内角\(A\)，\(B\)，\(C\)所对的边分别为\(a,b,c\)，已知\(\sin (A+C)=8{{\sin }^{2}}\dfrac{B}{2}\) ．
\((1)\)求\(\cos B\) ；

\((2)\)若\(a+c=6\)，\(\Delta ABC\)的面积为\(2\)，求\(b\)．

难度：较易

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2．

\(\sin\left( {-}\dfrac{10}{3}\pi \right)\) 的值等于\(\left( { } \right)\)

A．\(\dfrac{1}{2}\)

B．\({-}\dfrac{1}{2}\)

C．\(\dfrac{\sqrt{3}}{2}\)

D．\({-}\dfrac{\sqrt{3}}{2}\)

难度：较易

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3．

已知\({\sin }\left( \alpha +\dfrac{\pi }{6} \right)=\dfrac{2\sqrt{5}}{5}\)，则\({\cos }\left( \dfrac{\pi }{3}-\alpha \right)=\)( )

A．\(\dfrac{\sqrt{5}}{5}\)

B．\(-\dfrac{\sqrt{5}}{5}\)

C．\(\dfrac{2\sqrt{5}}{5}\)

D．\(-\dfrac{2\sqrt{5}}{5}\)

难度：较难

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4．
已知角\(\alpha\)的终边经过点\(P(m{,}2\sqrt{2}){,}\sin\alpha{=}\dfrac{2\sqrt{2}}{3}\)且\(\alpha\)为第二象限．
\((1)\)求\(m\)的值；
\((2)\)若\(\tan\beta{=}\sqrt{2}\)，求\(\dfrac{\sin\alpha\cos\beta{+}3\sin(\dfrac{\pi}{2}{+}\alpha)\sin\beta}{\cos(\pi{+}\alpha)\cos({-}\beta){-}3\sin\alpha\sin\beta}\)的值．

难度：难

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5．

化简\(\sin 600^{\circ}\)的值是( )

A．\(\dfrac{1}{2}\)

B．\(-\dfrac{1}{2}\)

C．\(\dfrac{\sqrt{3}}{2}\)

D．\(-\dfrac{\sqrt{3}}{2}\)

难度：较易

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6．

已知\(\alpha ∈\left( \dfrac{3}{2}π,2π\right) \)，且满足\(\cos \left( \alpha +\dfrac{2017}{2}\pi \right)=\dfrac{3}{5}\)，则\(\sin \alpha +\cos \alpha = \)( )

A．\(- \dfrac{7}{5} \)

B．\(- \dfrac{1}{5} \)

C．\(\dfrac{1}{5}\)

D．\(\dfrac{7}{5}\)

难度：中等

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7．

若\(\sin (\dfrac{{ }\!\!\pi\!\!{ }}{4}-x)=-\dfrac{1}{5}\)，则\(\cos (\dfrac{5{ }\!\!\pi\!\!{ }}{4}+x)\)的值等于\((\) \()\)

A．\(-\dfrac{\sqrt{24}}{5}\)

B．\(-\dfrac{1}{5}\)

C．\(\dfrac{1}{5}\)

D．\(\dfrac{\sqrt{24}}{5}\)

难度：中等

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8．

已知\(\sin(\dfrac{\pi}{4}{+}\alpha){=}\dfrac{2}{3}\)，则\(\cos(\dfrac{\pi}{4}{-}\alpha)\)的值等于\(({ })\)

A．\({-}\dfrac{2}{3}\)

B．\(\dfrac{2}{3}\)

C．\(\dfrac{\sqrt{5}}{3}\)

D．\({±}\dfrac{\sqrt{5}}{3}\)

难度：较难

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9．

\(\tan \left( -\dfrac{23}{6}\pi \right)=\)

A．\(-\sqrt{3}\)

B．\(\sqrt{3}\)

C．\(-\dfrac{\sqrt{3}}{3}\)

D．\(\dfrac{\sqrt{3}}{3}\)

难度：较难

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10．
已知\(\cos (\dfrac{\pi }{4}+x)=\dfrac{3}{5},\dfrac{17}{12}\pi < x < \dfrac{7}{4}\pi \)，则\(\dfrac{\sin 2x+2{{\sin }^{2}}x}{1-\tan x}\)的值为__________。

难度：难

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