1、阶段强化练(三),第四章 三角函数、解三角形,一、选择题 1.(2019福建闽侯五校期中联考)sin215cos215等于,解析 sin215cos215(cos215sin215),1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,故选C.,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,故选A.,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,1,2,3,4,5,6,7,8,9,
2、10,11,12,13,14,15,16,17,18,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,解析 由图易知xOA，xOB.,故选B.,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,1,2,3,4,5,6,7,8,9,10,11,12,
3、13,14,15,16,17,18,由f(x1)f(x2)0可得x1，x2是函数的极值点，,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,2，f(x)sin(2x)，,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,令2k2x2k，kZ，kxk，kZ，,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,解析 由函数f(x)的最小正周期为，可求得2，,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,1,2,3,4,5,6,7,8,
4、9,10,11,12,13,14,15,16,17,18,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,由正弦定理，得sin Acos Bcos Asin B2sin Ccos C， sin(AB)sin C2sin Ccos C，,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,所以f(x)在区间(，2)内单调，,1,2,3,4,
5、5,6,7,8,9,10,11,12,13,14,15,16,17,18,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,二、填空题 13.(2019陕西四校联考)已知sin 2cos ，则cos 2_.,解析 由已知得tan 2，cos 2cos2sin2,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,解析 根据三角函数诱导公式，得,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,15.(2019武汉示范高中联考)函数ysin xcos x2sin xcos x的最
6、大值为 _.,解析 令tsin xcos x，则tsin xcos x,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,16.(2019银川一中月考)已知函数f(x)cos xsin x(xR)，则下列四个命题中正确的是_.(写出所有正确命题的序号) 若f(x1)f(x2)，则x1x2； f(x)的最小正周期是2；,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,解析 f(x1)f(x2)，,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,错误；,由f(x)的图象可知，
7、正确；,故填.,(1)求f(x)的解析式；,三、解答题,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,18.(2019福建闽侯五校期中联考)已知向量a( sin x，cos x)，b(cos x， cos x)，f(x)ab. (1)求f(x)的最小正周期和单调递增区间；,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,f(x)的最小正周期是.,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,