已知函数f(x)=sinx+sin(x+2/3π)(x∈R )(1)函数y=f(x)的图像的二相邻对称轴之间的距离 (2)函数f(x)=1/3,求cos(2x+2/3π)的值 注:
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![已知函数f(x)=sinx+sin(x+2/3π)(x∈R )(1)函数y=f(x)的图像的二相邻对称轴之间的距离 (2)函数f(x)=1/3,求cos(2x+2/3π)的值 注:](/uploads/image/z/102306-66-6.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3Dsinx%2Bsin%EF%BC%88x%2B2%2F3%CF%80%29%28x%E2%88%88R+%29%EF%BC%881%EF%BC%89%E5%87%BD%E6%95%B0y%3Df%28x%29%E7%9A%84%E5%9B%BE%E5%83%8F%E7%9A%84%E4%BA%8C%E7%9B%B8%E9%82%BB%E5%AF%B9%E7%A7%B0%E8%BD%B4%E4%B9%8B%E9%97%B4%E7%9A%84%E8%B7%9D%E7%A6%BB+%EF%BC%882%EF%BC%89%E5%87%BD%E6%95%B0f%28x%29%3D1%2F3%2C%E6%B1%82cos%282x%2B2%2F3%CF%80%29%E7%9A%84%E5%80%BC+%E6%B3%A8%3A)
已知函数f(x)=sinx+sin(x+2/3π)(x∈R )(1)函数y=f(x)的图像的二相邻对称轴之间的距离 (2)函数f(x)=1/3,求cos(2x+2/3π)的值 注:
已知函数f(x)=sinx+sin(x+2/3π)(x∈R )
(1)函数y=f(x)的图像的二相邻对称轴之间的距离 (2)函数f(x)=1/3,求cos(2x+2/3π)的值 注:
已知函数f(x)=sinx+sin(x+2/3π)(x∈R )(1)函数y=f(x)的图像的二相邻对称轴之间的距离 (2)函数f(x)=1/3,求cos(2x+2/3π)的值 注:
f(x)=sinx+sin(x+2π/3)
=simx+simxcos2π/3+cosxsin2π/3
=sinx-1/2sinx+√3/2cosx
=1/2sinx+√3/2cosx
=sin(x+π/3)
(1)∵T=2π,∴相邻两个对称轴之间的距离是π;
(2)f(x)=1/3,即sin(x+π/3)=1/3,
∴cos(2x+2π/3)=cos2(x+π/3)=1-2sin²(x+π/3)=1-2/9=7/9
(1)f(x)=sinx-1/2sinx+√3/2cosx=1/2sinx+√3/2cosx=sin(x+π/3)
∴最小正周期T=2π
∴二相邻对称轴之间的距离:T/2=π
(2)f(x)=sin(x+π/3)=1/3
∴cos(2x+2π/3)=1-2sin²(x+π/3)=1-1/9=8/9
(1)f(x)=sinx+sinx*(-1/2)+根号3/2cosx
=1/2sinx+根号3/2cosx
=sin(x+π/3)
则周期为2π,两相邻对称轴之间距离为π
(2)f(x)=sin(x+Pai/3)=1/3
推出cos(2x+2π/3)=1-2(sin(x+π/3))^2=7/9第一...
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(1)f(x)=sinx+sinx*(-1/2)+根号3/2cosx
=1/2sinx+根号3/2cosx
=sin(x+π/3)
则周期为2π,两相邻对称轴之间距离为π
(2)f(x)=sin(x+Pai/3)=1/3
推出cos(2x+2π/3)=1-2(sin(x+π/3))^2=7/9
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