共50条信息
已知\(f\left( \alpha \right)=\dfrac{\tan (-\alpha -\pi ){{\sin }^{2}}(-\alpha -\pi )}{\sin (\alpha -\dfrac{\pi }{2})\cos (\dfrac{\pi }{2}+\alpha )\tan (\pi -\alpha )}\).
\((1)\)化简\(f\left( \alpha \right)\);
\((2)\)若\(f\left( \alpha \right)=2\),求\(\dfrac{3\sin \alpha +\cos \alpha }{2\sin \alpha -\cos \alpha }\)的值.
已知函数\(f(x)=5 \sqrt{3}\sin (π-x)+5\sin ( \dfrac{π}{2}+x)+5 \).\((1)\)求函数\(f(x)\)的对称轴与对称中心;
\((2)\)函数\(f(x)\)的图像向右平移\(\dfrac{π}{6} \)个单位长度,再向下平移\(a(a > 0)\)个单位长度后,再把横坐标压缩到原来的一半,得到函数\(g(x)\)的图像,且函数\(g(x)\)的最大值为\(2\),求函数\(g(x)\)的解析式和单调区间。
已知函数\(f\left(x\right)=4\tan x\sin \left( \dfrac{π}{2}-x\right)\cos \left(x- \dfrac{π}{3}\right)- \sqrt{3} \)
\((1)\)求\(f\left(x\right) \)的定义域与最小正周期;
\((2)\)讨论\(f\left(x\right) \)在区间\(\left[- \dfrac{π}{4}, \dfrac{π}{4}\right] \)上的单调性。
已知\(f(x)= \dfrac{\cos ^{2}(nπ+x)·\sin ^{2}(nπ-x)}{\cos ^{2}[(2n+1)π-x]}(n∈Z)\).
\((1)\)化简\(f(x)\)的表达式;
\((2)\)求\(f\left( \left. \dfrac{π}{2 016} \right. \right)+f\left( \left. \dfrac{1 007π}{2 016} \right. \right)\)的值.
已知角\(α \)的终边在第二象限,且与单位圆交于点\(P\left(m, \dfrac{ \sqrt{15}}{4}\right) \).
\((1)\)求实数\(m\)的值;
\((2)\)求\(\dfrac{\sin \left(α- \dfrac{π}{2}\right)}{\sin \left(π+α\right)-\sin \left( \dfrac{3π}{2}-α\right)+1} \)的值.
\((2)\)若\(a+c=6\),\(\Delta ABC\)的面积为\(2\),求\(b\).
已知\(\sin (\dfrac{3\pi }{2}+\theta )=\dfrac{1}{4}\),
求\(\dfrac{\cos (\pi +\theta )}{\cos \theta [\cos (\pi +\theta )-1]}+\dfrac{\cos (\theta -2\pi )}{\cos (\theta +2\pi )\cos (\theta +\pi )+\cos (-\theta )}\)的值。
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