在△ABC中A为锐角 a=2√3,c=4,f(A)为函数f(x)=(√3/2) sin2x- (1/2)cos2x+2在[0,∏/2]上最大值求A,b和△ABC的面积S
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![在△ABC中A为锐角 a=2√3,c=4,f(A)为函数f(x)=(√3/2) sin2x- (1/2)cos2x+2在[0,∏/2]上最大值求A,b和△ABC的面积S](/uploads/image/z/8580652-52-2.jpg?t=%E5%9C%A8%E2%96%B3ABC%E4%B8%ADA%E4%B8%BA%E9%94%90%E8%A7%92+a%3D2%E2%88%9A3%2Cc%3D4%2Cf%28A%29%E4%B8%BA%E5%87%BD%E6%95%B0f%28x%29%3D%28%E2%88%9A3%2F2%29+sin2x-+%281%2F2%29cos2x%2B2%E5%9C%A8%5B0%2C%E2%88%8F%2F2%5D%E4%B8%8A%E6%9C%80%E5%A4%A7%E5%80%BC%E6%B1%82A%2Cb%E5%92%8C%E2%96%B3ABC%E7%9A%84%E9%9D%A2%E7%A7%AFS)
在△ABC中A为锐角 a=2√3,c=4,f(A)为函数f(x)=(√3/2) sin2x- (1/2)cos2x+2在[0,∏/2]上最大值求A,b和△ABC的面积S
在△ABC中A为锐角 a=2√3,c=4,f(A)为函数f(x)=(√3/2) sin2x- (1/2)cos2x+2在[0,∏/2]上最大值
求A,b和△ABC的面积S
在△ABC中A为锐角 a=2√3,c=4,f(A)为函数f(x)=(√3/2) sin2x- (1/2)cos2x+2在[0,∏/2]上最大值求A,b和△ABC的面积S
sinA/(2√3)=sinC/4
2sinA=√3sinC
f(x)=(√3/2) sin2x- (1/2)cos2x+2=cos(-30)sin2x+sin(-3)cos2x+2=sin(2x-30)+2
xE[0,∏/2] 2xE[0,∏] 2x-∏/6E[-∏/6,5∏/6]
当2x-30=90 x=60(即∏/3)取最大值.
f(x)max=f(A)=f(∏/3)=1+2=3
此时:A=∏/3
所以2sin∏/3=√3sinC
2√3/2=√3sinC
sinC=1
C=90
B=90-60=30
S=1/2*ac(sinB)=1/2*2√3*4sin30=2根号3
f(x)=(√3/2) sin2x- (1/2)cos2x+2
=sin2xcos(π/6)-cos2xsinπ/6+2
=sin(2x-π/6)+2
当x=π/3时,sin(2x-π/6)=1;函数取最大值=3
所以,A=π/3
由正弦定理得:
a/sinA=c/sinC
sinC=csinA/a=4×√3/2÷(2√3)=1
所以...
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f(x)=(√3/2) sin2x- (1/2)cos2x+2
=sin2xcos(π/6)-cos2xsinπ/6+2
=sin(2x-π/6)+2
当x=π/3时,sin(2x-π/6)=1;函数取最大值=3
所以,A=π/3
由正弦定理得:
a/sinA=c/sinC
sinC=csinA/a=4×√3/2÷(2√3)=1
所以,C=π/2
B=π/2-π/3=π/6
b=c/2=4/2=2
△ABC的面积S=ab/2=2√3×2/2=2√3
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