高一必修四試題及答案

一、單項(xiàng)選擇題（每題2分，共20分）1.已知角\(\alpha\)終邊上一點(diǎn)\(P(-4,3)\)，則\(\sin\alpha\)的值為（）A.\(\frac{4}{5}\)B.\(-\frac{4}{5}\)C.\(\frac{3}{5}\)D.\(-\frac{3}{5}\)2.函數(shù)\(y=\sinx\)的最小正周期是（）A.\(\frac{\pi}{2}\)B.\(\pi\)C.\(2\pi\)D.\(4\pi\)3.已知\(\overrightarrow{a}=(1,2)\)，\(\overrightarrow=(-3,4)\)，則\(\overrightarrow{a}\cdot\overrightarrow\)的值為（）A.\(5\)B.\(-5\)C.\(11\)D.\(-11\)4.化簡\(\cos(\alpha-\beta)\cos\beta-\sin(\alpha-\beta)\sin\beta\)的結(jié)果是（）A.\(\cos\alpha\)B.\(\cos(\alpha-2\beta)\)C.\(\sin\alpha\)D.\(\sin(\alpha-2\beta)\)5.已知\(\tan\alpha=3\)，則\(\frac{\sin\alpha+\cos\alpha}{\sin\alpha-\cos\alpha}\)的值為（）A.\(2\)B.\(-2\)C.\(\frac{1}{2}\)D.\(-\frac{1}{2}\)6.函數(shù)\(y=\cos(2x+\frac{\pi}{3})\)的圖象的一條對稱軸方程是（）A.\(x=\frac{\pi}{3}\)B.\(x=\frac{\pi}{6}\)C.\(x=-\frac{\pi}{6}\)D.\(x=-\frac{\pi}{3}\)7.若\(\overrightarrow{AB}=(2,3)\)，\(\overrightarrow{AC}=(4,7)\)，則\(\overrightarrow{BC}\)等于（）A.\((-2,-4)\)B.\((2,4)\)C.\((6,10)\)D.\((-6,-10)\)8.已知\(\sin\alpha=\frac{1}{2}\)，\(\alpha\in(0,\frac{\pi}{2})\)，則\(\cos\alpha\)的值為（）A.\(\frac{\sqrt{3}}{2}\)B.\(-\frac{\sqrt{3}}{2}\)C.\(\frac{1}{2}\)D.\(-\frac{1}{2}\)9.函數(shù)\(y=\tanx\)的定義域是（）A.\(\{x|x\neqk\pi+\frac{\pi}{2},k\inZ\}\)B.\(\{x|x\neqk\pi,k\inZ\}\)C.\(\{x|x\neq2k\pi+\frac{\pi}{2},k\inZ\}\)D.\(\{x|x\neq2k\pi,k\inZ\}\)10.已知\(\overrightarrow{a}=(2,m)\)，\(\overrightarrow=(-1,2)\)，若\(\overrightarrow{a}\parallel\overrightarrow\)，則\(m\)的值為（）A.\(4\)B.\(-4\)C.\(1\)D.\(-1\)二、多項(xiàng)選擇題（每題2分，共20分）1.以下哪些是三角函數(shù)的基本性質(zhì)（）A.周期性B.奇偶性C.單調(diào)性D.有界性2.下列向量中，與\(\overrightarrow{a}=(1,-1)\)平行的向量有（）A.\(\overrightarrow=(-1,1)\)B.\(\overrightarrow{c}=(2,-2)\)C.\(\overrightarrowzr17tl7=(1,1)\)D.\(\overrightarrow{e}=(-2,2)\)3.對于\(y=\sin(2x+\frac{\pi}{6})\)，以下說法正確的是（）A.最小正周期是\(\pi\)B.圖象關(guān)于點(diǎn)\((\frac{5\pi}{12},0)\)對稱C.在\([-\frac{\pi}{6},\frac{\pi}{3}]\)上單調(diào)遞增D.圖象可由\(y=\sin2x\)向左平移\(\frac{\pi}{6}\)個(gè)單位得到4.已知\(\cos\alpha=\frac{1}{3}\)，\(\alpha\in(0,\pi)\)，則（）A.\(\sin\alpha=\frac{2\sqrt{2}}{3}\)B.\(\tan\alpha=2\sqrt{2}\)C.\(\sin(\alpha+\frac{\pi}{2})=\frac{1}{3}\)D.\(\cos(\alpha-\frac{\pi}{2})=\frac{2\sqrt{2}}{3}\)5.以下哪些是兩角和與差的三角函數(shù)公式（）A.\(\sin(A+B)=\sinA\cosB+\cosA\sinB\)B.\(\cos(A-B)=\cosA\cosB+\sinA\sinB\)C.\(\tan(A+B)=\frac{\tanA+\tanB}{1-\tanA\tanB}\)D.\(\sin(A-B)=\sinA\cosB-\cosA\sinB\)6.函數(shù)\(y=\cosx\)的圖象的對稱中心是（）A.\((k\pi,0)\)，\(k\inZ\)B.\((k\pi+\frac{\pi}{2},0)\)，\(k\inZ\)C.\((2k\pi,0)\)，\(k\inZ\)D.\((2k\pi+\frac{\pi}{2},0)\)，\(k\inZ\)7.已知向量\(\overrightarrow{a}=(x_1,y_1)\)，\(\overrightarrow=(x_2,y_2)\)，則下列運(yùn)算正確的是（）A.\(\overrightarrow{a}+\overrightarrow=(x_1+x_2,y_1+y_2)\)B.\(\overrightarrow{a}-\overrightarrow=(x_1-x_2,y_1-y_2)\)C.\(\lambda\overrightarrow{a}=(\lambdax_1,\lambday_1)\)（\(\lambda\inR\)）D.\(\overrightarrow{a}\cdot\overrightarrow=x_1x_2+y_1y_2\)8.下列函數(shù)中，是偶函數(shù)的有（）A.\(y=\cosx\)B.\(y=\sinx\)C.\(y=\cos2x\)D.\(y=\tanx\)9.已知\(\sin\alpha=\frac{3}{5}\)，則\(\cos2\alpha\)的值可能為（）A.\(\frac{7}{25}\)B.\(-\frac{7}{25}\)C.\(\frac{24}{25}\)D.\(-\frac{24}{25}\)10.對于向量\(\overrightarrow{a}\)，\(\overrightarrow\)，\(\overrightarrow{c}\)，下列說法正確的是（）A.\((\overrightarrow{a}+\overrightarrow)+\overrightarrow{c}=\overrightarrow{a}+(\overrightarrow+\overrightarrow{c})\)B.\(\overrightarrow{a}\cdot\overrightarrow=\overrightarrow\cdot\overrightarrow{a}\)C.若\(\overrightarrow{a}\cdot\overrightarrow=0\)，則\(\overrightarrow{a}=\overrightarrow{0}\)或\(\overrightarrow=\overrightarrow{0}\)D.\((\lambda\overrightarrow{a})\cdot\overrightarrow=\lambda(\overrightarrow{a}\cdot\overrightarrow)\)（\(\lambda\inR\)）三、判斷題（每題2分，共20分）1.函數(shù)\(y=\sinx\)在\([0,\pi]\)上單調(diào)遞增。（）2.向量\(\overrightarrow{a}=(1,2)\)與向量\(\overrightarrow=(2,4)\)平行。（）3.\(\cos(\frac{\pi}{2}-\alpha)=\sin\alpha\)。（）4.函數(shù)\(y=\tanx\)的圖象是中心對稱圖形。（）5.若\(\overrightarrow{a}\cdot\overrightarrow=0\)，則\(\overrightarrow{a}\perp\overrightarrow\)。（）6.函數(shù)\(y=\sin(2x+\frac{\pi}{3})\)的圖象可以由\(y=\sin2x\)向左平移\(\frac{\pi}{3}\)個(gè)單位得到。（）7.\(\sin^2\alpha+\cos^2\alpha=1\)對任意\(\alpha\)都成立。（）8.向量\(\overrightarrow{a}=(x_1,y_1)\)，\(\overrightarrow=(x_2,y_2)\)，若\(\overrightarrow{a}\parallel\overrightarrow\)，則\(x_1y_2-x_2y_1=0\)。（）9.函數(shù)\(y=\cosx\)的最大值是\(1\)，最小值是\(-1\)。（）10.已知\(\sin\alpha=\frac{1}{2}\)，則\(\alpha=\frac{\pi}{6}\)。（）四、簡答題（每題5分，共20分）1.求函數(shù)\(y=\sin(2x-\frac{\pi}{6})\)的單調(diào)遞增區(qū)間。-答案：令\(2k\pi-\frac{\pi}{2}\leq2x-\frac{\pi}{6}\leq2k\pi+\frac{\pi}{2},k\inZ\)，解不等式得\(k\pi-\frac{\pi}{6}\leqx\leqk\pi+\frac{\pi}{3},k\inZ\)，所以單調(diào)遞增區(qū)間是\([k\pi-\frac{\pi}{6},k\pi+\frac{\pi}{3}],k\inZ\)。2.已知\(\overrightarrow{a}=(3,-1)\)，\(\overrightarrow=(1,2)\)，求\(\overrightarrow{a}-2\overrightarrow\)。-答案：\(2\overrightarrow=(2,4)\)，則\(\overrightarrow{a}-2\overrightarrow=(3-2,-1-4)=(1,-5)\)。3.化簡\(\frac{\sin(\pi-\alpha)\cos(\frac{\pi}{2}+\alpha)}{\cos(\pi+\alpha)\sin(\frac{3\pi}{2}-\alpha)}\)。-答案：根據(jù)誘導(dǎo)公式，\(\sin(\pi-\alpha)=\sin\alpha\)，\(\cos(\frac{\pi}{2}+\alpha)=-\sin\alpha\)，\(\cos(\pi+\alpha)=-\cos\alpha\)，\(\sin(\frac{3\pi}{2}-\alpha)=-\cos\alpha\)，則原式\(=\frac{\sin\alpha(-\sin\alpha)}{(-\cos\alpha)(-\cos\alpha)}=-\tan^2\alpha\)。4.已知\(\tan\alpha=2\)，求\(\frac{3\sin\alpha+\cos\alpha}{\sin\alpha-2\cos\alpha}\)的值。-答案：分子分母同時(shí)除以\(\cos\alpha\)，原式變?yōu)閈(\frac{3\tan\alpha+1}{\tan\alpha-2}\)，把\(\tan\alpha=2\)代入得\(\frac{3\times2+1}{2-2}\)，分母為\(0\)，該式無意義。五、討論題（每題5分，共20分）1.討論三角函數(shù)在物理學(xué)中的應(yīng)用，舉例說明。-答案：在物理學(xué)中，三角函數(shù)應(yīng)用廣泛。如簡諧振動，位移隨時(shí)間變化\(x=A\sin(\omegat+\varphi)\)，描述物體振動狀態(tài)。交流電中，