已知f(x)=4cos(平方)x-4(根号3)asinxcosx,将f(x)的图像向右平移π/4,向下平移2个单位,平移后得函数g(x)的图像关于直线x=π/12对称 ⑴求实数a的值,⑵已知f(x-π/6)=2cosx - 2,求sin(平方)x+cosx的值答案:(1
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![已知f(x)=4cos(平方)x-4(根号3)asinxcosx,将f(x)的图像向右平移π/4,向下平移2个单位,平移后得函数g(x)的图像关于直线x=π/12对称 ⑴求实数a的值,⑵已知f(x-π/6)=2cosx - 2,求sin(平方)x+cosx的值答案:(1](/uploads/image/z/10207197-45-7.jpg?t=%E5%B7%B2%E7%9F%A5f%28x%29%3D4cos%28%E5%B9%B3%E6%96%B9%29x-4%28%E6%A0%B9%E5%8F%B73%29asinxcosx%2C%E5%B0%86f%28x%29%E7%9A%84%E5%9B%BE%E5%83%8F%E5%90%91%E5%8F%B3%E5%B9%B3%E7%A7%BB%CF%80%EF%BC%8F4%2C%E5%90%91%E4%B8%8B%E5%B9%B3%E7%A7%BB2%E4%B8%AA%E5%8D%95%E4%BD%8D%2C%E5%B9%B3%E7%A7%BB%E5%90%8E%E5%BE%97%E5%87%BD%E6%95%B0g%28x%29%E7%9A%84%E5%9B%BE%E5%83%8F%E5%85%B3%E4%BA%8E%E7%9B%B4%E7%BA%BFx%3D%CF%80%2F12%E5%AF%B9%E7%A7%B0+++%E2%91%B4%E6%B1%82%E5%AE%9E%E6%95%B0a%E7%9A%84%E5%80%BC%2C%E2%91%B5%E5%B7%B2%E7%9F%A5f%28x-%CF%80%2F6%29%3D2cosx+-+2%2C%E6%B1%82sin%28%E5%B9%B3%E6%96%B9%29x%2Bcosx%E7%9A%84%E5%80%BC%E7%AD%94%E6%A1%88%EF%BC%9A%EF%BC%881)
已知f(x)=4cos(平方)x-4(根号3)asinxcosx,将f(x)的图像向右平移π/4,向下平移2个单位,平移后得函数g(x)的图像关于直线x=π/12对称 ⑴求实数a的值,⑵已知f(x-π/6)=2cosx - 2,求sin(平方)x+cosx的值答案:(1
已知f(x)=4cos(平方)x-4(根号3)asinxcosx,将f(x)的图像向右平移π/4,向下平移2个单位,平移后得函数g(x)的图像关于直线x=π/12对称
⑴求实数a的值,⑵已知f(x-π/6)=2cosx - 2,求sin(平方)x+cosx的值
答案:
(1)a=1
(2)1或19/16
已知f(x)=4cos(平方)x-4(根号3)asinxcosx,将f(x)的图像向右平移π/4,向下平移2个单位,平移后得函数g(x)的图像关于直线x=π/12对称 ⑴求实数a的值,⑵已知f(x-π/6)=2cosx - 2,求sin(平方)x+cosx的值答案:(1
(1)
f(x)=4cos(平方)x-4(根号3)asinxcosx
=4cos²x-4√3asinxcosx
将f(x)的图像向右平移π/4,向下平移2个单位,
得函数g(x)= 4cos²(x-π/4)-4√3asin(x-π/4)cos(x-π/4)-2
=4*[1+cos2(x-π/4)]/2-2√3asin2(x-π/4)-2
= 2cos2(x-π/4) -2√3asin2(x-π/4)
=2sin2x+2√3acos2x,
g(x)的图像关于直线x=π/12对称,
则g(0)=g(π/6),
即2√3a=√3+√3a,
a=1.
(2)
a=1时,f(x) =4cos²x-4√3sinxcosx
=4*[1+cos2x]/2-2√3sin2x
=2cos2x-2√3sin2x+2
=4 cos(2x+π/3)+2,
所以f(x-π/6)= 4 cos(2(x-π/6)+π/3)+2
=4 cos2x+2,
已知f(x-π/6)=2cosx - 2,
所以4 cos2x+2=2cosx - 2,
4(2cos²x-1) +2=2cosx - 2,
8cos²x=2cosx,
Cosx=0或1/4.
∴sin²x+cosx=1- cos²x+cosx
=1或19/16.