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            • 1. 计算:
              (1)已知扇形的周长为10,面积是4,求扇形的圆心角.
              (2)已知扇形的周长为40,当他的半径和圆心角取何值时,才使扇形的面积最大?
            • 2.
              已知\(α=-1920^{\circ}\)
              \((1)\)将\(α\)写成\(β+2kπ(k∈Z,0\leqslant β < 2π)\)的形式,并指出它是第几象限角
              \((2)\)求与\(α\)终边相同的角\(θ\),满足\(-4π\leqslant θ < 0\).
            • 3.

              如图所示,角\(a\)的始边与\(x\)轴的非负半轴重合,终边与单位圆交于点\(A(x\)\({\,\!}_{1}\),\(y\)\({\,\!}_{1}\)\()\),将射线\(OA\)按逆时针方向旋转\(\dfrac{2\pi }{3}\)后与单位圆交于点\(B(x\)\({\,\!}_{2}\),\(y\)\({\,\!}_{2}\)\()\),\(f(a)=x\)\({\,\!}_{1}\)\(-x\)\({\,\!}_{2}\)

              \((1)\)若角\(a\)为锐角,求\(f(a)\)的取值范围;

              \((2)\)比较\(f(2)\)与\(f(3)\)的大小.

            • 4.
              如图,角\(α\)的始边与\(x\)轴的非负半轴重合,终边与单位圆交于点\(A\) \((x_{1},y_{l})\),将射线\(OA\)按逆时针方向旋转\( \dfrac {2π}{3}\)后与单位圆交于点\(B(x_{2},y_{2})\),\(f(a)=x_{l}-x_{2}\).
              \((\)Ⅰ\()\)若角\(α\)为锐角,求\(f(α)\)的取值范围;
              \((\)Ⅱ\()\)比较\(f(2)\)与\(f(3)\)的大小.
            • 5.

              已知\(α=1680^{\circ}\),

              \((1)\)把\(α\)表示成\(2kπ+β\)的形式\((k∈Z,β∈[0,2π))\).

              \((2)\)求\(θ\),使\(θ\)与\(α\)的终边相同,且\(θ∈(-4π,-2π)\).

            • 6.

              如图所示,角\(a\)的始边与\(x\)轴的非负半轴重合,终边与单位圆交于点\(A(x_{1},y_{1})\),将射线\(OA\)按逆时针方向旋转\(\dfrac{2\pi }{3}\)后与单位圆交于点\(B(x_{2},y_{2})\),\(f(a)=x_{1}-x_{2}\).

              \((1)\)若角\(a\)为锐角,求\(f(a)\)的取值范围;

              \((2)\)比较\(f(2)\)与\(f(3)\)的大小.

            • 7. 已知\(α=1690^{\circ}\),把\(α\)表示成\(2\) \(k\)\(π+β\)的形式\(( \)\(k\)\(∈Z\),\(β∈[0,2π))\).
            • 8.

              把下列各角化成\(2kπ+α (0\leqslant α < 2π,k∈Z)\)的形式,并指出是第几象限角


              \((1)-1 500^{\circ}\);                

              \((2)\dfrac{23}{6}π \);      

            • 9.

              \((1)\)若\(\tan α=-2\),且\(\sin α < 0\),则\(\cos α= \)____________.

              \((2)\)已知\(\sin (α- \dfrac{π}{4})= \dfrac{3}{5} \)则\(\cos (α+ \dfrac{π}{4}) \)的值为       

              \((3)\)函数\(y= \sqrt{1-2\cos x} \)的定义域为____________.

              \((4)\)关于函数\(f(x)=|\sin 2x|\)有下列命题:

              \(①\)函数\(f(x)\)的最小正周期为\(π\);

              \(②\)函数\(f(x)\)在区间\((0, \dfrac{π}{2} )\)上单调递增;

              \(③\)函数\(f(x)\)的对称轴是\(x= \dfrac{kπ}{2}+ \dfrac{π}{4},k∈Z \);  

                \(④\)若\(f(x_{1})=f(x_{2})=1\),则\(|{x}_{1}-{x}_{2}{|}_{min}= \dfrac{π}{6} \);

                     其中正确的序号为                  

            • 10.

              已知\(\alpha \)为三角形内角,若\(\sin \alpha +\cos \alpha =-\dfrac{1}{5}\),求

              \((1)\tan \alpha \);

              \((2)\dfrac{2\cos (\pi -\alpha )-3\sin (\pi +\alpha )}{4\cos (-\alpha )+\sin (2\pi -\alpha )}\).

            0/40

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