已知向量a=[√2sin(x/2-π/4),√3cosx/2]向量b=[√2sin(x/2+π/4),2sinx/2]函数f(x)=向量a·向量b1.求函数f(x)的对称轴方程及其单调递增区间2.在锐角△ABC中,若f(A)=2/3,求cosA的值(这题可答可不答)
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![已知向量a=[√2sin(x/2-π/4),√3cosx/2]向量b=[√2sin(x/2+π/4),2sinx/2]函数f(x)=向量a·向量b1.求函数f(x)的对称轴方程及其单调递增区间2.在锐角△ABC中,若f(A)=2/3,求cosA的值(这题可答可不答)](/uploads/image/z/10458444-12-4.jpg?t=%E5%B7%B2%E7%9F%A5%E5%90%91%E9%87%8Fa%3D%5B%E2%88%9A2sin%28x%2F2-%CF%80%2F4%29%2C%E2%88%9A3cosx%2F2%5D%E5%90%91%E9%87%8Fb%3D%5B%E2%88%9A2sin%28x%2F2%2B%CF%80%2F4%29%2C2sinx%2F2%5D%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%3D%E5%90%91%E9%87%8Fa%C2%B7%E5%90%91%E9%87%8Fb1.%E6%B1%82%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%E7%9A%84%E5%AF%B9%E7%A7%B0%E8%BD%B4%E6%96%B9%E7%A8%8B%E5%8F%8A%E5%85%B6%E5%8D%95%E8%B0%83%E9%80%92%E5%A2%9E%E5%8C%BA%E9%97%B42.%E5%9C%A8%E9%94%90%E8%A7%92%E2%96%B3ABC%E4%B8%AD%2C%E8%8B%A5f%EF%BC%88A%EF%BC%89%3D2%2F3%2C%E6%B1%82cosA%E7%9A%84%E5%80%BC%EF%BC%88%E8%BF%99%E9%A2%98%E5%8F%AF%E7%AD%94%E5%8F%AF%E4%B8%8D%E7%AD%94%EF%BC%89)
已知向量a=[√2sin(x/2-π/4),√3cosx/2]向量b=[√2sin(x/2+π/4),2sinx/2]函数f(x)=向量a·向量b1.求函数f(x)的对称轴方程及其单调递增区间2.在锐角△ABC中,若f(A)=2/3,求cosA的值(这题可答可不答)
已知向量a=[√2sin(x/2-π/4),√3cosx/2]向量b=[√2sin(x/2+π/4),2sinx/2]
函数f(x)=向量a·向量b
1.求函数f(x)的对称轴方程及其单调递增区间
2.在锐角△ABC中,若f(A)=2/3,求cosA的值(这题可答可不答)
已知向量a=[√2sin(x/2-π/4),√3cosx/2]向量b=[√2sin(x/2+π/4),2sinx/2]函数f(x)=向量a·向量b1.求函数f(x)的对称轴方程及其单调递增区间2.在锐角△ABC中,若f(A)=2/3,求cosA的值(这题可答可不答)
f(x)=a·b=√2sin(x/2-π/4)√2sin(x/2+π/4)+2√3cosx/2sinx/2
=2sin(x/2-π/4)sin[π/2-(π/4-x/2)]+2√3cosx/2sinx/2
=-2sin(x/2-π/4)cos(x/2-π/4)+√3sinx
=-sin(x-π/2)+√3sinx
=cosx+√3sinx
=2sin(x+π/6)
f(x)的对称轴:x+π/6=kπ
x=kπ-π/6
x+π/6在[kπ-π/2,2kπ+π/2]单调递增
x在[2kπ-2π/3,2kπ+π/3]单调递增
f(A)=2sin(x+π/6)=2/3
sin(x+π/6)=1/3
cos(x+π/6)=2√2/3
cosA=cosA[(x+π/6)-π/6]=√3/2cosA(x+π/6)+1/2sin(x+π/6)
=√3/2*2√2/3+1/2*1/3
=(1+√6)/6
被采纳的正确答案那位
cos(x)=cos(-x)是偶函数好嘛
sin[π/2-(π/4-x/2)]=cos(π/4-x/2),又cos(π/4-x/2)=cos(x/2-π/4)
所以f(x)=a·b=√2sin(x/2-π/4)√2sin(x/2+π/4)+2√3cosx/2sinx/2
=2sin(x/2-π/4)sin[π/2-(π/4-x/2)]+2√3c...
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被采纳的正确答案那位
cos(x)=cos(-x)是偶函数好嘛
sin[π/2-(π/4-x/2)]=cos(π/4-x/2),又cos(π/4-x/2)=cos(x/2-π/4)
所以f(x)=a·b=√2sin(x/2-π/4)√2sin(x/2+π/4)+2√3cosx/2sinx/2
=2sin(x/2-π/4)sin[π/2-(π/4-x/2)]+2√3cosx/2sinx/2
=2sin(x/2-π/4)cos(x/2-π/4)+√3sinx
负号是没有的好嘛!
最终应为√3sinx-cosx.
而且不用那么麻烦的,
x1x2=√2sin(x/2-π/4)√2sin(x/2+π/4)=2.√2/2(sinx/2-cosx/2)√2/2(sinx/2+cosx/2)
=(sinx/2-cosx/2)(sinx/2+cosx/2)=sin^(x/2)-cos^2(x/2)=-cosx
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