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1、高中数学试题三角函数单元测试题三角函数单元测试题 姓名, 班级, 考场, 座位号, 一、选择题(本大题共10小题，每小题5分，共50分) 1(下列函数中，最小正周期为的偶函数是 ( ) xA.y,sin2x B.y,cos 221,tanxC.y,sin2x，cos2x D.y, 21，tanx2(设函数y,cos(sinx)，则 ( ) A.它的定义域是,1，1, B.它是偶函数 C.它的值域是,cos1，cos1, D.它不是周期函数 3(把函数y,cosx的图象上的所有点的横坐标缩小到原来的一半，纵坐标扩大到原来的两倍，然后把图象向左平移 个单位.则所得图象表示的函数的解析式为 ( )
2、4A.y,2sin2x B.y,2sin2x xC.y,2cos(2x， ) D.y,2cos( ， ) 4244(函数y,2sin(3x, )图象的两条相邻对称轴之间的距离是 ( ) 424A. B. C. D. 3335(若sin，cos,m，且,2 ?m,1，则角所在象限是 ( ) A.第一象限 B.第二象限 C.第三象限 D.第四象限 36(函数y,|cotx|?sinx(0,x? 且x?)的图象是 ( ) 22cosx7(设y, ，则下列结论中正确的是 ( ) 1，sinxA.y有最大值也有最小值 B.y有最大值但无最小值 C.y有最小值但无最大值 D.y既无最大值又无最小值 int
3、egrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the citys liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning d
4、istrict, shale gas production capacity reached 277 million cubic metres, built the countrys first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue
5、growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for water and the second land of the seven hills. 236 meters to 2000 meters above sea level in the city, low m
6、ountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, old town-the Sou
7、th Bank Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile
8、, peripheral group centres service was weak and inadequate accounting for city development, suspicious pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, integrated energy, chemic
9、als and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the citys liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas pro
10、duction capacity reached 277 million cubic metres, built the countrys first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topograph
11、y terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for water and the second land of the seven hills. 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 4
12、5.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, old town-the South Bank Center constru
13、ction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group cen
14、tres service was weak and inadequate accounting for city development, suspicious pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, 8(函数y,sin( ,2x)的单调增区间是 ( ) 435A.,k, ，k， ,(k?Z)
15、B.,k， ，k， ,(k?Z) 8888337C.,k, ，k， ,(k?Z) D.,k， ，k， ,(k?Z) 8888129(已知0?x?，且, ,a,0，那么函数f(x),cosx,2asinx,1的最小值是 ( ) 2A.2a，1 B.2a,1 C.,2a,1 D.2a 10(求使函数y,sin(2x，)，3 cos(2x，)为奇函数，且在,0， ,上是增函数的的一个4值为 ( ) 542A. B. C. D. 3333二、填空题(本大题共6小题，每小题5分，共30分) cosx11(函数y, 的值域是_. 1，2cosxcosx (函数y, 的定义域是_. 12lg(1，tanx)
16、13(如果x，y?,0，,，且满足|sinx|,2cosy,2，则x,_，y,_. 14(已知函数y,2cosx，x?,0，2,和y,2，则它们的图象所围成的一个封闭的平面图形的面积是_ 15(函数y,sinx，cosx，sin2x的值域是_. (关于函数f(x),4sin(2x， )(x?R)有下列命题: 163?由f(x),f(x),0可得x,x必是的整数倍; 1212?y,f(x)的表达式可改为y,4cos(2x, ); 6?y,f(x)的图象关于点(, ，0)对称; 6?y,f(x)的图象关于直线x, 对称. 6其中正确的命题的序号是_. 三、解答题(本大题共5小题，共70分.解答应写
17、出文字说明、证明过程或演算步骤) 17(本小题满分12分)如图为函数y,Asin(x，)(A,0，,0)的图象的一部分，试求该函数的一个解析式. integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the citys liquor industry slip to stabilise. Promoting deep development
18、of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the countrys first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population.
19、2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for water and the second land of t
20、he seven hills. 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building w
21、ith an area of about 76.2km2. From city-building situation, old town-the South Bank Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre ha
22、s not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, suspicious pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, cent
23、ripetal city traffic organization has not changed, integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the citys liquor industry slip to stabilise. Promoting deep development of integrated energy,
24、advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the countrys first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figur
25、e 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for water and the second land of the seven hills. 236 me
26、ters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 7
27、6.2km2. From city-building situation, old town-the South Bank Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, fun
28、ctions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, suspicious pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic o
29、rganization has not changed, 2218(本小题满分14分)已知函数y,(sinx，cosx)，2cosx.(x?R) (1)当y取得最大值时，求自变量x的取值集合. (2)该函数图象可由y,sinx(x?R)的图象经过怎样的平移和伸缩变换得到, 19(本小题满分14分)已知函数f(x),log(sinx,cosx) 12(1)求它的定义域和值域;(2)求它的单调减区间; (3)判断它的奇偶性;(4)判断它的周期性，如果是周期函数，求出它的一个周期. integrated energy, chemicals and textile Yibin city, are th
30、e three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the citys liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 milli
31、on cubic metres, built the countrys first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, No
32、rth-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for water and the second land of the seven hills. 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 deve
33、lopment of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, old town-the South Bank Center construction is lagging behind, disintegr
34、ation of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequa
35、te accounting for city development, suspicious pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, integrated energy, chemicals and textile Yibin city, are the three core pillars o
36、f the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the citys liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built
37、 the countrys first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low
38、 mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for water and the second land of the seven hills. 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin lands
39、capes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, old town-the South Bank Center construction is lagging behind, disintegration of the old city
40、is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city
41、 development, suspicious pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, 20(本小题满分15分)某村欲修建一横断面为等腰梯形的水渠(如图)，为降低成本，必须尽量减少水与水渠壁的接触面.若水渠横断面面积设计为定值 m，渠深3米，则水渠侧壁的倾斜角应为多少时，方能使修建的成本最低,
42、 21( (本小题满分15分)已知函数f(x),sin(x，)(,0，0?)是R上的偶函数，其图3象关于点M( ，0)对称，且在区间,0， ,上是单调函数，求和的值. 42integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the citys liquor industry slip to stabilise. Promoting deep
43、 development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the countrys first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the
44、 population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for water and the sec
45、ond land of the seven hills. 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities
46、in building with an area of about 76.2km2. From city-building situation, old town-the South Bank Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southb
47、ank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, suspicious pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been ex
48、panding, centripetal city traffic organization has not changed, integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the citys liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the countrys first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to