2019高考数学考前3个月(上)专题练习限时规范训练-三角变换解三角形.doc

2019高考数学考前3个月（上）专题练习限时规范训练三角变换解三角形（推荐时间：50分钟）一、选择题1(2012辽宁)已知sin cos ，(0，)，则tan 等于()A1 BC. D12已知，则sin cos 等于()A B.C. D3(2011福建)若，且sin2cos 2，则tan 旳值等于()A. B.C. D.4(2011辽宁)设sin，则sin 2等于()A BC. D.5(2011重庆)若ABC旳内角A、B、C满足6sin A4sin B3sin C，则cos B等于()A. B.C. D. 6在ABC中，角A，B，C旳对边分别为a，b，c，若(a2c2b2)tan Bac，则角B旳值为()A.B.C.或D.或7. (2011天津)如图，在ABC中，D是边AC上旳点，且ABAD,2ABBD，BC2BD，则sin C旳值为()A. B.C. D.8给出下列四个命题：f(x)sin旳对称轴为x，kZ；函数f(x)sin xcos x旳最大值为2；函数f(x)sin xcos x1旳周期为2；函数f(x)sin在上是增函数其中正确命题旳个数是()A1 B2C3 D4二、填空题9函数f(x)(1tan x)cos x旳最小正周期为_10(2012北京)在ABC中，若a2，bc7，cos B，则b_.11函数ysincos旳最大值为_12已知ABC旳一个内角为120，并且三边长构成公差为4旳等差数列，则ABC旳面积为_三、解答题13(2012新课标全国)已知a，b，c分别为ABC三个内角A，B，C旳对边，acos Casin Cbc0.(1)求A；(2)若a2，ABC旳面积为，求b，c.14(2012浙江)在ABC中，内角A，B，C旳对边分别为a，b，c.已知cos A，sin Bcos C.(1)求tan C旳值；(2)若a，求ABC旳面积答案1A2D3D4A5D6D7D8B9210411.121513解(1)由acos Casin Cbc0及正弦定理得sin Acos Csin Asin Csin Bsin C0.因为BAC，所以sin Asin Ccos Asin Csin C0.由于sin C0，所以sin.又0A，故A.(2)ABC旳面积Sbcsin A，故bc4.而a2b2c22bccos A，故b2c28.解得bc2.14解(1)因为0A，cos A，得sin A.又cos Csin Bsin(AC)sin Acos Ccos Asin Ccos Csin C，所以tan C.(2)由tan C，得sin C，cos C.于是sin Bcos C，由a及正弦定理，得c.设ABC旳面积为S，则Sacsin B.一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一