已知函数f(x)=2sin(x+α/2)cos(x+α/2)+2√3cos^2(x+α/2)-√3,α为常数求函数f(x)的最小正周期
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![已知函数f(x)=2sin(x+α/2)cos(x+α/2)+2√3cos^2(x+α/2)-√3,α为常数求函数f(x)的最小正周期](/uploads/image/z/4018853-29-3.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3D2sin%28x%2B%CE%B1%2F2%29cos%28x%2B%CE%B1%2F2%29%2B2%E2%88%9A3cos%5E2%28x%2B%CE%B1%2F2%29-%E2%88%9A3%2C%CE%B1%E4%B8%BA%E5%B8%B8%E6%95%B0%E6%B1%82%E5%87%BD%E6%95%B0f%28x%29%E7%9A%84%E6%9C%80%E5%B0%8F%E6%AD%A3%E5%91%A8%E6%9C%9F)
已知函数f(x)=2sin(x+α/2)cos(x+α/2)+2√3cos^2(x+α/2)-√3,α为常数求函数f(x)的最小正周期
已知函数f(x)=2sin(x+α/2)cos(x+α/2)+2√3cos^2(x+α/2)-√3,α为常数
求函数f(x)的最小正周期
已知函数f(x)=2sin(x+α/2)cos(x+α/2)+2√3cos^2(x+α/2)-√3,α为常数求函数f(x)的最小正周期
f(x)=2sin(x+α/2)cos(x+α/2)+2√3cos^2(x+α/2)-√3
f(x)=sin(2x+α)+2√3[cos(2x+α)+1]/2-√3
f(x)=sin(2x+α)+√3[cos(2x+α)+1]-√3
=sin(2x+α)+√3cos(2x+α)
=2×[1/2sin(2x+α)+√3/2cos(2x+α)]
=2[sin(2x+α)·cosπ/3+cos(2x+α)·sinπ/3]
=2sin(2x+α+π/3) ∴ ω = 2
T=2π/|ω|=π
原函数=sin(2*(x+a/2))+√3cos(2*(x+a/2))=2*(1/2*sin(2*(x+a/2))+√3/2*cos(2*(x+a/2)))
=2*(cos(pi/3)*sin(2*(x+a/2))+sin(pi/3)*cos(2*(x+a/2)))
=2*sin(2*(x+a/2)+pi/3);
pi就是圆周率
f(x)=sin(2x+α)+2根3[1+cos(2x+α)]/2-根3
=sin(2x+α)+根3+根3cos(2x+α)-根3
=sin(2x+α)+根3cos(2x+α)
=2sin(2x+α+π/3)
∴T=2π/2=π