1.设函数f(x)=cos(2x+π/3)+sin(平方)x(1)求函数f(x)的最大值和最小正周期(2)设A,B,C,为三角形ABC的三个内角,若cosB=1/3,f(c/2)=-1/4,且C为锐角,求sinA2.设三角形的内角A,B,C的边长分别为a,b,c,cos(A-C)+cosB=3/2,b(
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/06 19:40:36
![1.设函数f(x)=cos(2x+π/3)+sin(平方)x(1)求函数f(x)的最大值和最小正周期(2)设A,B,C,为三角形ABC的三个内角,若cosB=1/3,f(c/2)=-1/4,且C为锐角,求sinA2.设三角形的内角A,B,C的边长分别为a,b,c,cos(A-C)+cosB=3/2,b(](/uploads/image/z/2037487-31-7.jpg?t=1.%E8%AE%BE%E5%87%BD%E6%95%B0f%28x%29%3Dcos%282x%2B%CF%80%2F3%29%2Bsin%28%E5%B9%B3%E6%96%B9%29x%281%29%E6%B1%82%E5%87%BD%E6%95%B0f%28x%29%E7%9A%84%E6%9C%80%E5%A4%A7%E5%80%BC%E5%92%8C%E6%9C%80%E5%B0%8F%E6%AD%A3%E5%91%A8%E6%9C%9F%282%29%E8%AE%BEA%2CB%2CC%2C%E4%B8%BA%E4%B8%89%E8%A7%92%E5%BD%A2ABC%E7%9A%84%E4%B8%89%E4%B8%AA%E5%86%85%E8%A7%92%2C%E8%8B%A5cosB%3D1%2F3%2Cf%28c%2F2%29%3D-1%2F4%2C%E4%B8%94C%E4%B8%BA%E9%94%90%E8%A7%92%2C%E6%B1%82sinA2.%E8%AE%BE%E4%B8%89%E8%A7%92%E5%BD%A2%E7%9A%84%E5%86%85%E8%A7%92A%2CB%2CC%E7%9A%84%E8%BE%B9%E9%95%BF%E5%88%86%E5%88%AB%E4%B8%BAa%2Cb%2Cc%2Ccos%28A%EF%BC%8DC%29%2BcosB%3D3%2F2%2Cb%28)
1.设函数f(x)=cos(2x+π/3)+sin(平方)x(1)求函数f(x)的最大值和最小正周期(2)设A,B,C,为三角形ABC的三个内角,若cosB=1/3,f(c/2)=-1/4,且C为锐角,求sinA2.设三角形的内角A,B,C的边长分别为a,b,c,cos(A-C)+cosB=3/2,b(
1.设函数f(x)=cos(2x+π/3)+sin(平方)x
(1)求函数f(x)的最大值和最小正周期
(2)设A,B,C,为三角形ABC的三个内角,若cosB=1/3,f(c/2)=-1/4,且C为锐角,求sinA
2.设三角形的内角A,B,C的边长分别为a,b,c,cos(A-C)+cosB=3/2,b(平方)=ac,求B
有3题(第一题有2小题),做一题给5分...
1.设函数f(x)=cos(2x+π/3)+sin(平方)x(1)求函数f(x)的最大值和最小正周期(2)设A,B,C,为三角形ABC的三个内角,若cosB=1/3,f(c/2)=-1/4,且C为锐角,求sinA2.设三角形的内角A,B,C的边长分别为a,b,c,cos(A-C)+cosB=3/2,b(
1.(1)
f(x)=cos(2x+π/3)+sin(平方)x
=1/2cos2x-根号3/2sin2x+sin(平方)x+1/2-1/2
=1/2cos2x-根号3/2sin2x-1/2cos2x+1/2
=-根号3/2sin2x+1/2
当x=π/4时,f(x)的最大值为(1-根号3)/2,最小正周期为π.
(2)
f(c/2)=-根号3/2sinC+1/2=1/4
解得sinC=根号3/6 ∴cosC=根号33/6
∵cosB=1/3
∴sinB=2*根号2/3
sinA=sin(2π -B-C)
=sin(B+C)
=sinBcosC+cosBsinC
代入=(2*根号66+根号3)/18
∴sinA=(2*根号66+根号3)/18
刚给你做了解答,希望对你有帮助。
http://hi.baidu.com/zhihuichengzhang/blog/item/3e4550da1a2cbb3b33fa1c16.html
2) cos(A-C)+cosB=cos(A-C)-cos(A+C)=cosAcosC+sinAsinC-cosAcosC+sinAsinC=2sinAsinC=3/2
:. sinAs...
全部展开
刚给你做了解答,希望对你有帮助。
http://hi.baidu.com/zhihuichengzhang/blog/item/3e4550da1a2cbb3b33fa1c16.html
2) cos(A-C)+cosB=cos(A-C)-cos(A+C)=cosAcosC+sinAsinC-cosAcosC+sinAsinC=2sinAsinC=3/2
:. sinAsinC=3/4
又: a/sinA=b/sinB=c/sinC=k , b^2=ac
:. b^2=sin^2B*k^2 a=sinA*k c=sinC*k代入上式得
:. sin^2B=sinA*sinC=3/4
=> B=60 或120^o
根据题设条件:cos(A-C)+cosB=3/2, 必有COSB>0, :. B=60^o
还可以求出A.C
代入cos(A-C)+cosB=3/2 得cos(A-C)=1 =》A=C=60
收起