三角单元测试&8226;练习题.doc

  三角单元测试·练习题

一、选择题((1)题～(10)题每题4分，(11)题～(15)题每题5分，共65分)

                                                                                                  [    ]
A．第一象限                                 B．第二象限
C．第三象限                                 D．第四象限

                                                                                                  [    ]
A．-2                                           B．-1
C．1                                             D．2
(3)假如sinxsiny=1，那么2cos(x+y)值等于                               [    ]
A．-2                                           B．0
C．2                                             D．±2

                                                                                                  [    ]

(5)函数f(x)=sin2x-cos2x最小正周期是                                     [    ]

C．2π                                          D．4π

                                                                                                  [    ]
A．[0，2]                                     B．[0，2)
C．(0， 2]                                    D．(0，2)

                                                                                                  [    ]
A．奇函数非偶函数
B．偶函数非奇函数
C．非奇非偶函数
D．既是奇函数又是偶函数

                                                                                                  [    ]

(9)下列函数中，周期为π函数是                                             [    ]

                                                                                                          [    ]

(11)已知点M(sinθ-cosθ，tgθ)在第一象限，则在[0，2π)内θ取值范围是      [    ]

                                                                                                  [    ]

(13)在斜三角形ABC中，若sinA=cosBcosC，那么下列四式值必为常数是       [    ]
A．sinB+sinC                                 B．cosB+cosC
C．tgB+tgC                                   D．ctgB+ctgC
(14)一种直角三角形三内角正弦值成等比数列，其最小内角为
                                                                                                  [    ]

(15)将函数y=f(x)图象上每一点纵坐标保持不变，横坐标扩大到原

y=3sinx图象相似，则函数y=f(x)体现式是                                    [    ]

C．f(x)=-3sin2x                            D．f(x)=-3cos2x
二、填空题(每题4分，共16分)

(17)函数f(x)=sinxcos2α-cosxsin2α图象有关y轴对称，则α=______．
(18)函数f(x)=11-8cosx-2sin2x最大值是______．

①由f(x1)=f(x2)=0，可得x1-x2=kπ(k∈Z)

其中对命题序号是______．
三、解答题(本题有6小题，共69分)
(20)(10分)已知角α顶点与直角坐标系原点重叠，始边在x轴

(23)(12分)求函数y=(sin3xsin3x+cos3xcos3x)·see22x+sin2x最小值．
(24)(12分)在△ABC中，a，b，c分别是内角A，B，C对边，

(25)(12分)已知△ABC中，三个内角A，B，C成等差数列，cosB

答案与提醒

一、
(1)D
(2)D
(3)A
(4)D
(5)B
(6)B
(7)A
(8)A
(9)C
(10)C
(11)B
(12)B
(13)C
(14)B
(15)D

提醒

(3)∵|sinx|≤1，|siny|≤1，由sinxsiny=1知sinx=1，siny=1或sinx=-1，siny=-1
当sinx=siny=1时，cosx=cosy=0，此时2cos(x+y)=2(cosxcosy-sinxsiny)=-2
当sinx=siny=-1时，cosx=cosy=0，2cos(x+y)=-2

(7)y=sin2x是奇函数，不是偶函数．

∴选C．

(11)点M(sinθ-cosθ，tgθ)在第一象限，
∴sinθ-cosθ＞0，且tgθ＞0
即sinθ＞cosθ，且tgθ＞0又θ∈[0，2π)

∵sinA=cosBcosC  ∴tgB+tgC=1(常数)
(14)设Rt△ABC中，∠C=90°，A＜B
依题意有：sinA，sinB，sinC成等比数列，则sin2B=sinAsinC=sinA
又sinB=cosA  ∴sinA=cos2A=1-sin2A

(15)把 f(x)=-3cos2x纵坐标不变，横坐标扩大到本来2倍，得函数

提醒

∴sin3θ+cos3θ=(sinθ+cosθ)(1-sinθcosθ)

(18)y=11-8cosx-2sin2x=2(cosx-2)2+1，|cosx|≤1，当cosx=-1时，ymax=19

(23)y=(sin3x·sinx·sin2x+cos3x·cosx·cos2x)·sec22x+sin2x
=[sin3x·sinx(1-cos2x)+cos3x·cosx·cos2x]·sec22x+sin2x
=[sin3x·sinx+cos2x(cos3x·cosx-sin3x·sinx)]·sec22x+sin2x

(24)∵a，b，c成等差数列，∴a+c=2b即

(25)∵A，B，C成等差数列，又A+B+C=π