设函数f(x)=cos(x+2π/3)+2(cosx/2)^2,x∈R(1)求f(x)的值域(2)记△ABC的内角A,B,C的对边分别是a,b,c若f(B)=1,b=1,c=根号3,求a的值
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![设函数f(x)=cos(x+2π/3)+2(cosx/2)^2,x∈R(1)求f(x)的值域(2)记△ABC的内角A,B,C的对边分别是a,b,c若f(B)=1,b=1,c=根号3,求a的值](/uploads/image/z/15104241-9-1.jpg?t=%E8%AE%BE%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%3Dcos%EF%BC%88x%2B2%CF%80%2F3%29%2B2%28cosx%2F2%29%5E2%2Cx%E2%88%88R%EF%BC%881%EF%BC%89%E6%B1%82f%EF%BC%88x%29%E7%9A%84%E5%80%BC%E5%9F%9F%EF%BC%882%EF%BC%89%E8%AE%B0%E2%96%B3ABC%E7%9A%84%E5%86%85%E8%A7%92A%2CB%2CC%E7%9A%84%E5%AF%B9%E8%BE%B9%E5%88%86%E5%88%AB%E6%98%AFa%2Cb%2Cc%E8%8B%A5f%EF%BC%88B%29%3D1%2Cb%3D1%2Cc%3D%E6%A0%B9%E5%8F%B73%2C%E6%B1%82a%E7%9A%84%E5%80%BC)
设函数f(x)=cos(x+2π/3)+2(cosx/2)^2,x∈R(1)求f(x)的值域(2)记△ABC的内角A,B,C的对边分别是a,b,c若f(B)=1,b=1,c=根号3,求a的值
设函数f(x)=cos(x+2π/3)+2(cosx/2)^2,x∈R
(1)求f(x)的值域
(2)记△ABC的内角A,B,C的对边分别是a,b,c若f(B)=1,b=1,c=根号3,求a的值
设函数f(x)=cos(x+2π/3)+2(cosx/2)^2,x∈R(1)求f(x)的值域(2)记△ABC的内角A,B,C的对边分别是a,b,c若f(B)=1,b=1,c=根号3,求a的值
1.
f(x)=cos(x+2π/3)+2(cosx/2)^2
=cosxcos(2π/3)-sinxsin(2π/3)+cosx+1
=(-1/2)*cosx-(√3/2)*sinx+cosx+1
=(1/2)*cosx-(√3/2)*sinx+1
=cosxcos(π/3)-sinxsin(π/3)+1
=cos(x+π/3)+1
所以值域是【0,2】
2.
f(B)=1
所以cos(B+π/3)+1=1
即cos(B+π/3)=0
所以B+π/3=kπ+π/2(k∈Z)
又B是三角形内角
那么0<B<π
所以B=π/6
由余弦定理有cosB=(a^2+c^2-b^2)/2ac=(a^2+3-1)/(2a√3)=cos(π/6)=√3/2
所以a^2-3a+2=0
所以a=1或a=2
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buzhidao
f(x)=cos(x+2π/3)+2(cosx/2)^2=1/2cos(x)-根号3/2sin(x)+cos(x)+1=3/2cos(x)-根号3/2sin(x)+1=根号3{根号3/2cos(x)-1/2sin(x)}+1=根号3cos(x+π/3)+1
1. f(x)的值域为【1,1+根号3】
2. f(B)=1 B=2π/3 sinB/sinC=c/b C=π/3 A=π/2 a=2