优优班--学霸训练营 > 知识点挑题
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            • 1.
              已知角\(α\)为第三象限角,且\(\tan α= \dfrac {3}{4}\),则\(\sin α+\cos α=(\)  \()\)
              A.\(- \dfrac {7}{5}\)
              B.\(- \dfrac {1}{5}\)
              C.\( \dfrac {1}{5}\)
              D.\( \dfrac {7}{5}\)
            • 2.
              若\(1+\sin θ \sqrt {\sin ^{2}θ}+\cos θ \sqrt {\cos ^{2}θ}=0\)成立,则\(θ\)不可能是\((\)  \()\)
              A.第二、三、四象限角
              B.第一、二、三象限角
              C.第一、二、四象限角
              D.第一、三、四象限角
            • 3.
              已知\(\sin α= \dfrac {4}{5}\),并且\(α\)是第二象限的角,那么\(\tan α\)的值等于\((\)  \()\)
              A.\(- \dfrac {4}{3}\)
              B.\(- \dfrac {3}{4}\)
              C.\( \dfrac {3}{4}\)
              D.\( \dfrac {4}{3}\)
            • 4.
              已知\( \dfrac {\sin α-\cos α}{2\sin \alpha +3\cos \alpha }= \dfrac {1}{5}\),求\(\tan α\)的值.
            • 5.
              若\(\sin α=- \dfrac {5}{13}\),且\(α\)为第四象限角,则\(\tan α\)的值等于 ______ .
            • 6.
              \((1)\)已知\(\tan α=3\),计算\( \dfrac {4\sin α-2\cos α}{5\cos \alpha +3\sin \alpha }\)的值.
              \((2)\)已知\(\tan θ=- \dfrac {3}{4}\),求\(2+\sin θ\cos θ-\cos ^{2}θ\)的值.
            • 7.
              已知\(\sin x+\sin y= \dfrac {1}{3}\),则\(u=\sin x+\cos ^{2}x\)的最小值是\((\)  \()\)
              A.\(- \dfrac {1}{9}\)
              B.\(-1\)
              C.\(1\)
              D.\( \dfrac {5}{4}\)
            • 8.
              已知\(α∈(0, \dfrac {π}{2})\),\(β∈( \dfrac {π}{2},π)\)且\(\sin (α+β)= \dfrac {3}{5}\),\(\cos β=- \dfrac {5}{13}\),求\(\sin α\)的值.
            • 9.
              已知\(α\)是第四象限角,\(\tan α=- \dfrac {5}{12}\),则\(\sin α=(\)  \()\)
              A.\( \dfrac {1}{5}\)
              B.\( \dfrac {5}{13}\)
              C.\(- \dfrac {5}{13}\)
              D.\(- \dfrac {1}{5}\)
            • 10.
              已知\(f(α)= \dfrac {\sin (π+α)\cos (2π-α)\tan (-α)}{\tan (-\pi -\alpha )\cos ( \dfrac {3π}{2}+\alpha )}\).
              \((1)\)化简\(f(α)\);
              \((2)\)当\(α=- \dfrac {31π}{3}\)时,求\(f(α)\)的值;
              \((3)\)若\(α\)是第三象限的角,且\(\sin α=- \dfrac {1}{5}\),求\(f(α)\)的值.
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