共50条信息
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.
\((\)Ⅰ\()\;①\) 证明两角和的余弦公式\({C}_{α+β}:\cos (α+β)=\cos α\cos β-\sin α\sin β \);
\(\;②\) 证明:\(\sin 3\alpha =3{{\sin }^{2}}\alpha -4{{\sin }^{3}}\alpha \).
\((\)Ⅱ\()\) 已知\(\triangle ABC\)的面积\(S= \dfrac{1}{2}, \overrightarrow{AB}· \overrightarrow{AC}=3 \), 且\(\cos B= \dfrac{3}{5} \), 求\(\cos C\).
\((\)Ⅱ\()\alpha +2\beta \)的值.
如图,在平面直角坐标系\(xoy\)中,点\(A\left( {{x}_{1}},{{y}_{1}} \right)\),\(B\left( {{x}_{2}},{{y}_{2}} \right)\)在单位圆上,\(\angle xOA=\alpha \),\(α∈\left( \dfrac{π}{6}, \dfrac{π}{2}\right) \),\(\angle AOB=\dfrac{\pi }{3}\).
\((1)\)若\({\cos }\left( \alpha +\dfrac{\pi }{4} \right)=-\dfrac{3}{5}\),求\({{x}_{1}}\)的值;
\((2)\)过点\(A\)作\(x\)轴的垂线交单位圆于另一点\(C\),过\(B\)作\(x\)轴的垂线,垂足为\(D\),记\(\Delta AOC\)的面积为\({{S}_{1}}\),\(\Delta BOD\)的面积为\({{S}_{2}}\),设\(f\left( \alpha \right)={{S}_{1}}+{{S}_{2}}\),求函数\(f\left( \alpha \right)\)的最大值.
已知角\(α\)的终边上一点\(P(-15a,8a)(a∈R\)且\(a\neq 0)\),求\(α\)的各三角函数值.
如图,在平面直角坐标系\(XOY\)中,以\(X\)轴正半轴为始边的锐角\(\alpha \)与钝角\(\beta \)的终边与单位圆分别交于点\(A,B\)两点,\(X\)轴正半轴与单位\({{S}_{\Delta OAM}}=\dfrac{\sqrt{5}}{5}\)圆交于点\(M\),已知,点\(B\)的纵坐标是\(\dfrac{\sqrt{2}}{10}\)。
\((1)\)求\(\cos (\alpha -\beta )\)的值;
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