已知定义在R上的函数f(x)=Acos(wx+φ)(A>0,w>0,-π/2≤φ≤π/2,最大值与最小值的差为4相邻两个最低点之间的距离为π,且函数y=sin(2x+π/3)图像所有对称中心都在y=f(x)图像的对称轴上(1)求f(x
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![已知定义在R上的函数f(x)=Acos(wx+φ)(A>0,w>0,-π/2≤φ≤π/2,最大值与最小值的差为4相邻两个最低点之间的距离为π,且函数y=sin(2x+π/3)图像所有对称中心都在y=f(x)图像的对称轴上(1)求f(x](/uploads/image/z/7116352-16-2.jpg?t=%E5%B7%B2%E7%9F%A5%E5%AE%9A%E4%B9%89%E5%9C%A8R%E4%B8%8A%E7%9A%84%E5%87%BD%E6%95%B0f%28x%29%3DAcos%28wx%2B%CF%86%29%28A%EF%BC%9E0%2Cw%EF%BC%9E0%2C-%CF%80%2F2%E2%89%A4%CF%86%E2%89%A4%CF%80%2F2%2C%E6%9C%80%E5%A4%A7%E5%80%BC%E4%B8%8E%E6%9C%80%E5%B0%8F%E5%80%BC%E7%9A%84%E5%B7%AE%E4%B8%BA4%E7%9B%B8%E9%82%BB%E4%B8%A4%E4%B8%AA%E6%9C%80%E4%BD%8E%E7%82%B9%E4%B9%8B%E9%97%B4%E7%9A%84%E8%B7%9D%E7%A6%BB%E4%B8%BA%CF%80%2C%E4%B8%94%E5%87%BD%E6%95%B0y%3Dsin%282x%2B%CF%80%2F3%EF%BC%89%E5%9B%BE%E5%83%8F%E6%89%80%E6%9C%89%E5%AF%B9%E7%A7%B0%E4%B8%AD%E5%BF%83%E9%83%BD%E5%9C%A8y%3Df%EF%BC%88x%EF%BC%89%E5%9B%BE%E5%83%8F%E7%9A%84%E5%AF%B9%E7%A7%B0%E8%BD%B4%E4%B8%8A%EF%BC%881%EF%BC%89%E6%B1%82f%EF%BC%88x)
已知定义在R上的函数f(x)=Acos(wx+φ)(A>0,w>0,-π/2≤φ≤π/2,最大值与最小值的差为4相邻两个最低点之间的距离为π,且函数y=sin(2x+π/3)图像所有对称中心都在y=f(x)图像的对称轴上(1)求f(x
已知定义在R上的函数f(x)=Acos(wx+φ)(A>0,w>0,-π/2≤φ≤π/2,最大值与最小值的差为4
相邻两个最低点之间的距离为π,且函数y=sin(2x+π/3)图像所有对称中心都在y=f(x)图像的对称轴上
(1)求f(x)的表达式
(2)若f(x./2)=3/2(x∈[-π/2,π/2],求cos(x.-π/3)的值
(3)设向量a=(f(x-π/6),1),向量b=(1,cosx),x∈(0.π/2),若向量a*向量b+3≥.恒成立,求实数m的取值范围
已知定义在R上的函数f(x)=Acos(wx+φ)(A>0,w>0,-π/2≤φ≤π/2,最大值与最小值的差为4相邻两个最低点之间的距离为π,且函数y=sin(2x+π/3)图像所有对称中心都在y=f(x)图像的对称轴上(1)求f(x
1.)A-(-A)=4,A=2
相邻两个最低点之间的距离为π,即周期为π,所以2π/w=π,w=2
sin(2x+π/3)=cos(2x-π/6)
f(x)=2cos(2x+φ)
y=cosx的对称轴与对称中心相差π/2
所以2x+φ-(2x-π/6)=π/2
所以φ=π/3
所以 f(x)=2cos(2x+π/3)
2.)f(x./2)=2cos(x.+π/3)=3/2 cos(x.+π/3)=3/4 所以
sin(x.+π/3)=+-(根号7)/4
cos(x.-π/3)=cos(x.+π/3 -.2π/3)
=cos(x.+π/3)cos(2π/3)+sin(x.+π/3)sin( -2.π/3)
=-1/2cos(x.+π/3)- (根号3)/2*sin(x.+π/3)
=-3/8+-(根号21)/8
第三问有问题