共50条信息
已知\(f(x)=\sin (x+\dfrac{\pi }{2})\),\(g(x)=\sin (π-x)\),则下列结论中正确的是\((\) \()\)
在\(\Delta ABC\)中,已知\(a\sin B\cos C+c\sin B\cos A=\dfrac{1}{2}b\),且\(a > b\),其中内角\(A,B,C\)的对边分别为\(a,b,c\),则\(B=\)_________.
若\(\sin(\pi{+}\alpha){=}\dfrac{2}{3}\),则\(\cos 2\alpha\)的值为\(({ })\)
已知\(\sin (3{ }\!\!\pi\!\!{ }-\theta )=\dfrac{\sqrt{5}}{2}\sin (\dfrac{{ }\!\!\pi\!\!{ }}{2}+\theta )(\theta \in \mathbf{R})\),则\(\cos (\theta -\dfrac{{ }\!\!\pi\!\!{ }}{3})=\)________.
为了得到函数\(y=\sin (2x- \dfrac{π}{6} )\)的图象,可以将函数\(y=\cos 2x\)的图象( )
已知函数\(f(x)=\sin ( \dfrac{π}{2}-x)\sin x- \sqrt{3}{\cos }^{2}x= \dfrac{ \sqrt{3}}{2} \)
\((1)\)求\(f(x)\)的最大值以及取得最大值时的\(x\)值;
\((2)\)若方程\(f(x)= \dfrac{2}{3} \)在\((,π)\)上的解为\({x}_{1},{x}_{2} \),求\(\cos ({x}_{1}-{x}_{2}) \)的值
已知\(f\left( \alpha \right)=\dfrac{\cos \left( \dfrac{\pi }{2}+\alpha \right)\cdot \cos \left( 2\pi -\alpha \right)\cdot \sin \left( -\alpha +\dfrac{3}{2}\pi \right)}{\sin \left( -\pi -\alpha \right)\sin \left( \dfrac{3}{2}\pi +\alpha \right)}\) .
\((1)\)化简\(f\left( \alpha \right)\);\((2)\)若\(\alpha \)是第三象限角,且\(\cos \left( \alpha -\dfrac{3}{2}\pi \right)=\dfrac{1}{5}\),求\(f\left( \alpha \right)\)的值.
若\(\cos \left( \dfrac{π}{2}-α\right)=- \dfrac{1}{3} \),则\({{\sin }^{2}}\alpha -{{\cos }^{2}}\alpha =\) .
若\(\cos \alpha =-\dfrac{2}{3}\),则\(\dfrac{\cos (4\pi -\alpha )\sin (-\alpha )}{\sin (\dfrac{\pi }{2}+\alpha )\tan (\pi -\alpha )}\)的值为 .
\(\cos \dfrac{2π}{3}= \) _____________
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