2023学年高考数学大二轮复习能力升级练六解三角形文2.docxVIP免费

能力升级练(六)解三角形一、选择题1.在△ABC中,AB=5,AC=3,BC=7,则∠BAC=()A.π6B.π3C.2π3D.5π6解析在△ABC中,设AB=c=5,AC=b=3,BC=a=7,由余弦定理,得cos∠BAC=b2+c2-a22bc=9+25-4930=-12,由A∈(0,π),得A=2π3,即∠BAC=23π.答案C2.△ABC的内角A,B,C的对边分别为a,b,c.已知a=❑√5,c=2,cosA=23,则b=()A.❑√2B.❑√3C.2D.3解析由余弦定理,得5=b2+22-2×b×2×23,解得b=3,或b=-13(舍去).答案D3.(2023山东潍坊一模)若角α的终边过点A(2,1),则sin(32π-α)=()1A.-2❑√55B.-❑√55C.❑√55D.2❑√55解析由三角函数定义,cosα=2❑√5=25❑√5,则sin(32π-α)=-cosα=-2❑√55.答案A4.若tanθ=-13,则cos2θ=()A.-45B.-15C.15D.45解析cos2θ=cos2θ-sin2θ=cos2θ-sin2θcos2θ+sin2θ=1-tan2θ1+tan2θ=45.答案D5.(20...