高中数学试题三角函数单元测试题

高中数学 试题 中考模拟试题doc幼小衔接 数学试题 下载云南高中历年会考数学试题下载N4真题下载党史题库下载 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π的偶函数是 ( ) xA.y,sin2x B.y,cos 2 21,tanxC.y,sin2x，cos2x D.y, 21，tanx 2(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， π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 ( ) 4 A.y,2sin2x B.y,,2sin2x πxπC.y,2cos(2x， ) D.y,2cos( ， ) 424 π4(函数y,2sin(3x, )图象的两条相邻对称轴之间的距离是 ( ) 4 π2π4πA. B. C.π D. 333 5(若sinα，cosα,m，且,2 ?m,,1，则α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 3π6(函数y,|cotx|?sinx(0,x? 且x?π)的图象是 ( ) 2 2cosx7(设y, ，则下列结论中正确的是 ( ) 1，sinx A.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 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 city's 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 country's 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 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 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, 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 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, 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 city's 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 country's 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 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 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, 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 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, π8(函数y,sin( ,2x)的单调增区间是 ( ) 4 3πππ5πA.,kπ, ，kπ， ,(k?Z) B.,kπ， ，kπ， ,(k?Z) 8888 π3π3π7πC.,kπ, ，kπ， ,(k?Z) D.,kπ， ，kπ， ,(k?Z) 8888 129(已知0?x?π，且, ,a,0，那么函数f(x),cosx,2asinx,1的最小值是 ( ) 2 A.2a，1 B.2a,1 C.,2a,1 D.2a π10(求使函数y,sin(2x，θ)，3 cos(2x，θ)为奇函数，且在,0， ,上是增函数的θ的一个4 值为 ( ) 5π4π2ππA. 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_____________. 1，2cosx cosx (函数y, 的定义域是_____________. 12lg(1，tanx) 13(如果x，y?,0，π,，且满足|sinx|,2cosy,2，则x,___________，y,___________. 14(已知函数y,2cosx，x?,0，2π,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_____________. π(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π的整数倍; 1212 π?y,f(x)的表达式可改为y,4cos(2x, ); 6 π?y,f(x)的图象关于点(, ，0)对称; 6 π?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(ωx，φ)(A,0，ω,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 city's 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 country's 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 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 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, 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 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, 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 city's 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 country's 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 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 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, 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 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, 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) 1 2 (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 the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's 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 country's 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 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 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, 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 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, 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 city's 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 country's 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 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 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, 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 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, 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α应为多少时，方能使修建的成本最低, 21( (本小题满分15分)已知函数f(x),sin(ωx，φ)(ω,0，0?φ?π)是R上的偶函数，其图 3ππ象关于点M( ，0)对称，且在区间,0， ,上是单调函数，求φ和ω的值. 42 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 city's 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 country's 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 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 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, 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 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, 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 city's 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 country's 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 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 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, 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 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, 三角函数单元测试题答案 一、选择题(本大题共10小题，每小题5分，共50分) 1(D 2(B 3(B 4(A 5(C 6(C 7(C 8(D 9(C 10(C 二、填空题(本大题共6小题，每小题5分，共30分) 1ππ11((,?， ,?,1，+?) 12({x|, ，2kπ,x,2kπ或2kπ,x, ，2kπ(k?Z)} 342 513(x,0或π，y,0 14(4π 15({y,, ?y?1，2 } 16(?? 4 三、解答题(本大题共5小题，共70分.解答应写出文字说明、证明过程或演算步骤) 17((本小题满分12分)如图为函数y,Asin(ωx，φ)(A,0，ω,0)的图象的一部分，试求该 函数的一个解析式. 【解】 由图可得:A,3 ，T,2,MN,,π. π2从而ω, ,2，故y,3 sin(2x，φ) T π2π将M( ，0)代入得sin( ，φ),0 33 2π2π取φ,, 得y,3 sin(2x, ) 33 π5 ，0)代入y,3 sin(2x+φ) 【评注】 本题若将N(6 5π5π5π2π则可得:sin( ，φ),0.若取φ,, ，则y,3 sin(2x, ),,3 sin(2x, )， 3333 π它与y,3 sin(2x, )的图象关于x轴对称，故求解错误～因此，将点的坐标代入函数y,3 3 sin(2x，φ)后，如何确定φ，要看该点在曲线上的位置.如:M在上升的曲线上，就相当于“五 2π点法”作图中的第一个点，故 ，φ,0;而N点在下降的曲线上，因此相当于“五点法”作图3 5π2π中的第三个点，故 ，φ,π，由上可得φ的值均为, . 33 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, π2【解】 y,1，sin2x，2cosx,sin2x，cos2x，2,2 sin(2x， )，2. 4 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 city's 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 country's 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 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 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, 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 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, 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 city's 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 country's 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 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 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, 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 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, π(1)要使y取得最大值，则sin(2x， ),1. 4 πππ即:2x， ,2kπ， x,kπ， (k?Z) ,428 π?所求自变量的取值集合是{x,x,kπ， ，k?Z}. 8 (2)变换的步骤是: ππ?把函数y,sinx的图象向左平移 个单位，得到函数y,sin(x+ )的图象; 44 1π?将所得的图象上各点的横坐标缩短到原来的 倍(纵坐标不变)，得函数y,sin(2x， )24的图象; ?再将所得的图象上各点的纵坐标伸长到原来的2 倍(横坐标不变)，得函数 y,2 πsin(2x， )的图象; 4 π?最后将所得的图象向上平移2个单位，就得到 y,2 sin(2x， )+2的图象. 4 【说明】 以上变换步骤不唯一～ 19((本小题满分14分)已知函数f(x),(sinx,cosx) log1 2 (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. 【分析】 研究复合函数的性质(定义域、值域、单调性、奇偶性、周期性)应同时考虑内层函数与外层函数各自的特性以及它们的相互制约关系. π【解】 (1)由题意得sinx,cosx,0，即2 sin(x, ),0 4 ππ5π从而得2kπ,x, ,2kπ，π，所以函数的定义域为(2kπ， ，2kπ， )(k?Z) 444 π?0,sin(x, )?1，?0,sinx,cosx?2 4 11loglog即有(sinx,cosx)?2 ,, .故函数的值域是,, ，+?). 112222 ππ(2)?sinx,cosx,2 sin(x, )在f(x)的定义域上的单调递增区间为(2kπ， ，2kπ443ππ3π， )(k?Z)，函数f(x)的递减区间为(2kπ， ，2kπ， )(k?Z). 444 (3)?f(x)的定义域在数轴上对应的点不关于原点对称， ?函数f(x)是非奇非偶函数. 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 city's 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 country's 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 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 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, 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 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, 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 city's 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 country's 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 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 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, 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 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, (4)f(x，2π),,sin(x，2π),cos(x，2π),,(sinx,cosx),f(x). loglog11 22 ?函数f(x)是周期函数，2π是它的一个周期. 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α应为多少时，方能使修建的成本最低, 【分析】 本题中水与水渠壁的接触面最小，即是修建的 成本最低，而水与水渠壁的接触面最小，实际上是使水渠横断 面的周长 最小. 【解】 设水渠横断面的周长为y，则: 313×3(y,2× )×3，2× ? ,m sinα22tanα 2,cosαm即:y, ，3? (0?,α,90?). 3sinα 2,cosα欲减少水与水渠壁的接触面，只要使水渠横断面周长y最小，即要使t, sinα(0?,α,90?)最小， ?tsinα，cosα,2. 21?sin(α，φ), ，(其中φ由tanφ, ，φ?(0?，90?)) 2tt，1 22由 ?1得:t?3t?3 ,2t，1 3当且仅当t,3 ，即tanφ,，即φ,30?时，不等式取等号，此时sin(α，30?),1α,3 ,60?. 【答】 水渠侧壁的倾斜角α,60?时，修建成本最低. 21( (本小题满分15分)已知函数f(x),sin(ωx，φ)(ω,0，0?φ?π)是R上的偶函数，其图 3ππ象关于点M( ，0)对称，且在区间,0， ,上是单调函数，求φ和ω的值. 42 【解】 由f(x)是偶函数，得f(x),f(,x) 即sin(ωx，φ),sin(,ωx，φ) ?,cosφsinωx,cosφsinωx对任意x都成立. π且ω,0，?cosφ,0，依题设0?φ?π，?φ, 2 3π由f(x)的图象关于点M( ，0)对称，得， 4 3π3π3π取x,0，得f( ),,f( )，?f( ),0 444 3π3ωππ3ωπ?f( ),sin( ， ),cos ,0，又ω,0 4424 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 city's 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 country's 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 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 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, 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 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, 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 city's 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 country's 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 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 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, 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 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, 3ωππ2? , ，kπ，k,0，1，2，…，ω, (2k，1)，k,0，1，2，… 423 22ππ当k,0时，ω, ，f(x),sin( x， )在区间,0， ,上是减函数; 3322 ππ当k,1时，ω,2，f(x),sin(2x， )在区间,0， ,上是减函数; 22 10ππ当k?2时，ω? ，f(x),sin(ωx， )在区间,0， ,上不是单调函数; 322 2所以，ω, 或ω,2. 3 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 city's 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 country's 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 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 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, 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 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, 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 city's 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 country's 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 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 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, 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 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,