F(x)=(根号3/2)sin2x-cos^2x-1/2.1.当x属于【-π/12,5π/12】,f(x)的最值.2.三角形ABC,对应边abc.c=根号3,f(C)=0 .向量m=(1.sinA)与向量n=(2.sinB)共线,求a ,b.
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![F(x)=(根号3/2)sin2x-cos^2x-1/2.1.当x属于【-π/12,5π/12】,f(x)的最值.2.三角形ABC,对应边abc.c=根号3,f(C)=0 .向量m=(1.sinA)与向量n=(2.sinB)共线,求a ,b.](/uploads/image/z/6852191-23-1.jpg?t=F%28x%29%3D%28%E6%A0%B9%E5%8F%B73%2F2%29sin2x-cos%5E2x-1%2F2.1.%E5%BD%93x%E5%B1%9E%E4%BA%8E%E3%80%90-%CF%80%2F12%2C5%CF%80%2F12%E3%80%91%2Cf%EF%BC%88x%EF%BC%89%E7%9A%84%E6%9C%80%E5%80%BC.2.%E4%B8%89%E8%A7%92%E5%BD%A2ABC%2C%E5%AF%B9%E5%BA%94%E8%BE%B9abc.c%3D%E6%A0%B9%E5%8F%B73%2Cf%28C%29%3D0+.%E5%90%91%E9%87%8Fm%3D%281.sinA%29%E4%B8%8E%E5%90%91%E9%87%8Fn%3D%282.sinB%29%E5%85%B1%E7%BA%BF%2C%E6%B1%82a+%2Cb.)
F(x)=(根号3/2)sin2x-cos^2x-1/2.1.当x属于【-π/12,5π/12】,f(x)的最值.2.三角形ABC,对应边abc.c=根号3,f(C)=0 .向量m=(1.sinA)与向量n=(2.sinB)共线,求a ,b.
F(x)=(根号3/2)sin2x-cos^2x-1/2.
1.当x属于【-π/12,5π/12】,f(x)的最值.
2.三角形ABC,对应边abc.c=根号3,f(C)=0 .向量m=(1.sinA)与向量n=(2.sinB)共线,求a ,b.
F(x)=(根号3/2)sin2x-cos^2x-1/2.1.当x属于【-π/12,5π/12】,f(x)的最值.2.三角形ABC,对应边abc.c=根号3,f(C)=0 .向量m=(1.sinA)与向量n=(2.sinB)共线,求a ,b.
1、由公式cos2x=2(cosx)^2 -1
即(cosx)^2=0.5cos2x +0.5可知,
f(x)=√3/2 sin2x -0.5cos2x -1
=sin(2x-π/6) -1
x属于[-π/12,5π/12],所以2x-π/6属于[-π/3,2π/3]
显然当2x-π/6=π/2,即x=π/3时,f(x)取最大值,f(π/3)=sin(π/2)-1=0
当2x-π/6= -π/3,即x= -π/12时,f(x)取最小值,f(-π/12)=sin(-π/3)-1= -0.5√3 -1
2、f(C)=0,即sin(2C-π/6)=1,
所以2C-π/6=π/2,解得C=π/3,
而向量m=(1,sinA)与向量n=(2,sinB)共线,
即sinB/sinA=2,
A+B+C=π,C=π/3
所以B=2π/3 -A
故sin(2π/3 -A) /sinA=2,
而sin(2π/3 -A)=sin(2π/3)cosA -cos(2π/3)sinA=0.5√3cosA +0.5sinA
于是(0.5√3cosA +0.5sinA) /sinA
= 0.5√3cotA+0.5=2
解得cotA=√3,即A=π/6,
故B=2π/3 -A=π/2,
所以a=c×tanA=√3×tan(π/6)=1,
b=a/ sinA=1/sin(π/6)=2