共50条信息
用单位圆证明角\(α\)的正弦的绝对值与余弦的绝对值之和不小于\(1\),即已知\(0\leqslant α < 2π\),求证:\(|\sin α|+|\cos α|\geqslant 1\).
利用三角函数线,比较下列各组三角函数值的大小.
\((1)\sin \dfrac{2π}{3}\)与\(\sin \dfrac{4π}{5}\);
\((2)\tan \dfrac{2π}{3}\)与\(\tan \dfrac{4π}{5}\).
已知函数\(f(x)=\sqrt{3}\cos (2x-\dfrac{\pi }{3})-2\sin x\cos x\).
\((I)\)求\(f\)\((\)\(x\)\()\)的最小正周期;
\((II)\)求证:当\(x\in [-\dfrac{\pi }{4},\dfrac{\pi }{4}]\)时,\(f\left( x \right)\geqslant -\dfrac{1}{2}\).
如图所示,已知\(\alpha \)的终边所在直线上的一点\(P\)的坐标为\((-3,4)\),\(\beta \)的终边在第一象限且与单位圆的交点\(Q\)的纵坐标为\(\dfrac{\sqrt{2}}{10}\)
\((1)\)求\(\tan (2\alpha +\beta )\)的值
\((2)\)若\(\dfrac{\pi }{2} < \alpha < \pi ,0 < \beta < \dfrac{\pi }{2}\),求\(\alpha +\beta \)
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