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www.5k6b.com:2019高考数学二轮复习第二编专题三三角函数解三角形与平面向量第1讲三角函数的图象与性质习题课件文_图文

第二编 讲专题 专题三 三角函数、解三角形与平面向量 第1讲 三角函数的图象与性质 一、选择题 1.已知 α 为锐角,且 sinα=45,则 cos(π+α)=( ) A.-35 B.35 C.-45 D.45 解析 因为 α 为锐角,且 sinα=45,所以 cosα=35.所以 cos(α+π)=-cosα=-35. 2.函数 f(x)=tan????2x-3π????的单调递增区间是( ) A.????k2π-1π2,k2π+51π2????(k∈Z) B.????k2π-1π2,k2π+51π2????(k∈Z) C.????kπ-1π2,kπ+51π2????(k∈Z) D.????kπ-6π,kπ+152π????(k∈Z) 解析 当 kπ - π 2 <2x - π3 <kπ + π 2 (k ∈ Z) 时, 函数 y= tan????2x-π3????单调递增,解得k2π-1π2<x<k2π+152π(k∈Z),所以函 数 y=tan????2x-π3????的单调递增区间是????k2π-1π2,k2π+51π2????(k∈Z), 故选 B. 3.(2018·河南信阳月考)已知函数 f(x)=sin????2x+32π????(x∈ R),下面结论错误的是( ) A.函数 f(x)的最小正周期为 π B.函数 f(x)是偶函数 C.函数 f(x)的图象关于直线 x=π4对称 D.函数 f(x)在区间????0,2π????上是增函数 解析 f(x)=sin????2x+32π????=-cos2x,故其最小正周期为 π,故 A 正确;易知函数 f(x)是偶函数,B 正确;由函数 f(x) =-cos2x 的图象可知,函数 f(x)的图象的对称轴为直线 x =k2π(k∈Z),C 错误;由函数 f(x)的图象易知,函数 f(x)在????0,2π???? 上是增函数,D 正确,故选 C. 4.(2018·河北冀州中学月考)若函数 f(x)=2sinωx(ω>0) 的图象在(0,2π)上恰有一个极大值和一个极小值,则 ω 的取 值范围是( ) A.????34,1???? C.????34,45???? B.????1,54???? D.????34,54???? 解析 因为函数 f(x)=2sinωx(ω>0)的图象在(0,2π)上恰 有一个极大值和一个极小值,所以 ??? 34×2ωπ<2π, ????54×2ωπ≥2π, ω∈????34,54????,故选 D. 5.(2018·山东临沂模拟)函数 f(x)=x+coxsx的图象为 () 解析 函数 f(x)的定义域为(-∞,0)∪(0,+∞),故排 除 D;因为 f(-x)=(-x)+cos-?-x x?=-????x+coxsx????=-f(x), π 所以函数 f(x)为奇函数,故排除 B;又 f????π2????=π2+coπs2=π2>0, 2 故排除 C,故选 A. 6.将函数 f(x)=sin2x+ 3cos2x 的图象上的所有点向右 平移π6个单位长度,得到函数 g(x)的图象,则 g(x)图象的一 个对称中心是( ) A.????π3,0???? C.????-1π2,0???? B.????π4,0???? D.????π2,0???? 解析 将函数 f(x)=sin2x+ 3cos2x=2sin????2x+π3????图象 上所有的点向右平移π6个单位长度,得到函数 g(x)=2sin2x 的图象.函数 g(x)图象的对称中心横坐标满足 2x=kπ(k∈Z), 即 x=k2π(k∈Z).结合选项知应选 D. 7.如图,函数 f(x)=Asin(2x+φ)????A>0,|φ|<π2????的图象过 点(0, 3),则 f(x)的函数解析式为( ) A.f(x)=2sin????2x-3π???? B.f(x)=2sin????2x+π3???? C.f(x)=2sin????2x+π6???? D.f(x)=2sin????2x-6π???? 解析 由题意知,A=2,函数 f(x)的图象过点(0, 3), 所以 f(0)=2sinφ= 3, 由 |φ|< π 2 , 得 φ = π 3 , 所 以 f(x) = 2sin????2x+π3????.故选 B. 8.为了得到函数 y=sin????2x-6π????的图象,可以将函数 y =cos2x 的图象( ) A.向右平移π6个单位长度 B.向右平移π3个单位长度 C.向左平移π6个单位长度 D.向左平移π3个单位长度 解析 ∵y=sin????2x-π6????=cos????π2-????2x-π6????????=cos????23π-2x????= cos????2x-23π????=cos????2????x-π3????????,∴将函数 y=cos2x 的图象向右平 移π3个单位长度,故选 B. 9.(2018·河南洛阳统考)已知 f(x)=asin2x+bcos2x,其 中 a,b∈R,ab≠0.若 f(x)≤????f????π6????????对一切 x∈R 恒成立,且 f????π2???? >0,则 f(x)的单调递增区间是( ) A.????kπ-3π,kπ+6π????(k∈Z) B.????kπ+π6,kπ+23π????(k∈Z) C.????kπ,kπ+π2????(k∈Z) D.????kπ-2π,kπ????(k∈Z) 解析 f(x)=asin2x+bcos2x= a2+b2sin(2x+φ),其中 tanφ=ba.∵f(x)≤????f????π6????????,∴x=π6是函数 f(x)图象的一条对称轴, 即π3+φ=π2+kπ(k∈Z)

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