f(x)=(根号3/2)sin2x-(cosx)平方 -1/2 求f(x)的最小值f(x)=〔(根号3)/2〕sin2x-(cosx)平方 -1/2 (1):求f(x)的最小值和最小正周期 (2):设三角形ABC的内角ABC的对边为abc,且c=根号3,f(C)=0 若2sinA=sinB 求a,b的值
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![f(x)=(根号3/2)sin2x-(cosx)平方 -1/2 求f(x)的最小值f(x)=〔(根号3)/2〕sin2x-(cosx)平方 -1/2 (1):求f(x)的最小值和最小正周期 (2):设三角形ABC的内角ABC的对边为abc,且c=根号3,f(C)=0 若2sinA=sinB 求a,b的值](/uploads/image/z/2575688-32-8.jpg?t=f%28x%29%3D%28%E6%A0%B9%E5%8F%B73%2F2%29sin2x-%EF%BC%88cosx%EF%BC%89%E5%B9%B3%E6%96%B9+-1%2F2+%E6%B1%82f%28x%29%E7%9A%84%E6%9C%80%E5%B0%8F%E5%80%BCf%28x%29%3D%E3%80%94%28%E6%A0%B9%E5%8F%B73%29%2F2%E3%80%95sin2x-%EF%BC%88cosx%EF%BC%89%E5%B9%B3%E6%96%B9+-1%2F2+%281%29%3A%E6%B1%82f%28x%29%E7%9A%84%E6%9C%80%E5%B0%8F%E5%80%BC%E5%92%8C%E6%9C%80%E5%B0%8F%E6%AD%A3%E5%91%A8%E6%9C%9F+%282%29%3A%E8%AE%BE%E4%B8%89%E8%A7%92%E5%BD%A2ABC%E7%9A%84%E5%86%85%E8%A7%92ABC%E7%9A%84%E5%AF%B9%E8%BE%B9%E4%B8%BAabc%2C%E4%B8%94c%3D%E6%A0%B9%E5%8F%B73%2Cf%28C%29%3D0+%E8%8B%A52sinA%3DsinB+%E6%B1%82a%2Cb%E7%9A%84%E5%80%BC)
f(x)=(根号3/2)sin2x-(cosx)平方 -1/2 求f(x)的最小值f(x)=〔(根号3)/2〕sin2x-(cosx)平方 -1/2 (1):求f(x)的最小值和最小正周期 (2):设三角形ABC的内角ABC的对边为abc,且c=根号3,f(C)=0 若2sinA=sinB 求a,b的值
f(x)=(根号3/2)sin2x-(cosx)平方 -1/2 求f(x)的最小值
f(x)=〔(根号3)/2〕sin2x-(cosx)平方 -1/2 (1):求f(x)的最小值和最小正周期 (2):设三角形ABC的内角ABC的对边为abc,且c=根号3,f(C)=0 若2sinA=sinB 求a,b的值
f(x)=(根号3/2)sin2x-(cosx)平方 -1/2 求f(x)的最小值f(x)=〔(根号3)/2〕sin2x-(cosx)平方 -1/2 (1):求f(x)的最小值和最小正周期 (2):设三角形ABC的内角ABC的对边为abc,且c=根号3,f(C)=0 若2sinA=sinB 求a,b的值
(1)
f(x)=√3/2×sin2x-cos²x-1/2
=√3/2×sin2x-(2cos²x-1)/2-1
=√3/2×sin2x-cos2x/2-1
=sin2x×cosπ/6-cos2x×sinπ/6 -1
=sin(2x-π/6) -1
-1≤sin(2x-π/6)≤1,最小正周期=π
所以,f(x)的最小值=-1-1=-2,最小正周期=π
(2)
f(C)=0
f(C)=sin(2C-π/6)-1=0
sin(2C-π/6)=1
2C-π/6=π/2
2C=2π/3
C=π/3
sinB=2sinA
所以,b=2a
cosC=(a²+b²-c²)/2ab
所以,1/2=(5a²-3)/4a²
4a²=10a²-6
a²=1
a=1或a=-1(舍去)
b=2a=2
所以,a=1,b=2