已知函数y=2sinωxcosωx+2√3cos2ωx-√3(ω>0),直线x=x1、x=x2是y=f(x)的任意两条对称轴,其中绝对值x1-x2的最小值为π/2(1)求ω的值(2)若f(a)=2/3,求sin(5π/6-4a)的值,
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![已知函数y=2sinωxcosωx+2√3cos2ωx-√3(ω>0),直线x=x1、x=x2是y=f(x)的任意两条对称轴,其中绝对值x1-x2的最小值为π/2(1)求ω的值(2)若f(a)=2/3,求sin(5π/6-4a)的值,](/uploads/image/z/10752116-68-6.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0y%3D2sin%CF%89xcos%CF%89x%2B2%E2%88%9A3cos2%CF%89x-%E2%88%9A3%EF%BC%88%CF%89%EF%BC%9E0%EF%BC%89%2C%E7%9B%B4%E7%BA%BFx%3Dx1%E3%80%81x%3Dx2%E6%98%AFy%3Df%EF%BC%88x%EF%BC%89%E7%9A%84%E4%BB%BB%E6%84%8F%E4%B8%A4%E6%9D%A1%E5%AF%B9%E7%A7%B0%E8%BD%B4%2C%E5%85%B6%E4%B8%AD%E7%BB%9D%E5%AF%B9%E5%80%BCx1-x2%E7%9A%84%E6%9C%80%E5%B0%8F%E5%80%BC%E4%B8%BA%CF%80%2F2%281%29%E6%B1%82%CF%89%E7%9A%84%E5%80%BC%EF%BC%882%EF%BC%89%E8%8B%A5f%EF%BC%88a%EF%BC%89%3D2%2F3%2C%E6%B1%82sin%EF%BC%885%CF%80%2F6-4a%EF%BC%89%E7%9A%84%E5%80%BC%2C)
已知函数y=2sinωxcosωx+2√3cos2ωx-√3(ω>0),直线x=x1、x=x2是y=f(x)的任意两条对称轴,其中绝对值x1-x2的最小值为π/2(1)求ω的值(2)若f(a)=2/3,求sin(5π/6-4a)的值,
已知函数y=2sinωxcosωx+2√3cos2ωx-√3(ω>0),直线x=x1、x=x2是y=f(x)的任意两条对称轴,其中绝对值x1-x2的最小值为π/2
(1)求ω的值(2)若f(a)=2/3,求sin(5π/6-4a)的值,
已知函数y=2sinωxcosωx+2√3cos2ωx-√3(ω>0),直线x=x1、x=x2是y=f(x)的任意两条对称轴,其中绝对值x1-x2的最小值为π/2(1)求ω的值(2)若f(a)=2/3,求sin(5π/6-4a)的值,
y = sqrt(13) sin(2wx+A) - sqrt(3)
2w(x1-x2) = 2pi,A = arctan(2sqrt(3))
w = 2
f(a) = sqrt(13)sin(4a+A) -sqrt(3) = 2/3
4a + A =arcsin[ (2/3+sqrt(3))/sqrt(13)] = B
sin(5pi/6 - 4a) = sin(5pi/6 + A - arcsin(...) = sin5pi/6 cos(A-B) + cos5pi/6 sin(A-B)
= 1/2 [cosAcosB+sinAsinB -sinAcosB + cosAsinB]
= ...
= 0.5469
(你可以推导出精确值)
y = 2sinωxcosωx + 2√3cos²ωx - √3
= sin2ωx + √3cos2ωx
= sin(2ωx + π/3)
对称轴:
2ωx + π/3 = kπ + π/2
x = (kπ + π/6) / (2ω)
min∣x1 - x2∣= π / (2ω) = π/2
ω = 1