已知函数f(x)=sin(wx+Ф)(w>0,0≤Ф≤π)为偶函数图像上相邻的两个最高点之间的距离为2π.(1)求f(x)的解析式(2)若α∈(-π/3,π/2),且f(α+π/3)=1/3,求sin(2α+5π/3)的值
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![已知函数f(x)=sin(wx+Ф)(w>0,0≤Ф≤π)为偶函数图像上相邻的两个最高点之间的距离为2π.(1)求f(x)的解析式(2)若α∈(-π/3,π/2),且f(α+π/3)=1/3,求sin(2α+5π/3)的值](/uploads/image/z/1858967-71-7.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3Dsin%28wx%2B%D0%A4%29%EF%BC%88w%EF%BC%9E0%2C0%E2%89%A4%D0%A4%E2%89%A4%CF%80%EF%BC%89%E4%B8%BA%E5%81%B6%E5%87%BD%E6%95%B0%E5%9B%BE%E5%83%8F%E4%B8%8A%E7%9B%B8%E9%82%BB%E7%9A%84%E4%B8%A4%E4%B8%AA%E6%9C%80%E9%AB%98%E7%82%B9%E4%B9%8B%E9%97%B4%E7%9A%84%E8%B7%9D%E7%A6%BB%E4%B8%BA2%CF%80.%EF%BC%881%EF%BC%89%E6%B1%82f%28x%29%E7%9A%84%E8%A7%A3%E6%9E%90%E5%BC%8F%EF%BC%882%EF%BC%89%E8%8B%A5%CE%B1%E2%88%88%28-%CF%80%2F3%2C%CF%80%2F2%29%2C%E4%B8%94f%28%CE%B1%2B%CF%80%2F3%29%3D1%2F3%2C%E6%B1%82sin%282%CE%B1%2B5%CF%80%2F3%29%E7%9A%84%E5%80%BC)
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已知函数f(x)=sin(wx+Ф)(w>0,0≤Ф≤π)为偶函数图像上相邻的两个最高点之间的距离为2π.(1)求f(x)的解析式(2)若α∈(-π/3,π/2),且f(α+π/3)=1/3,求sin(2α+5π/3)的值
已知函数f(x)=sin(wx+Ф)(w>0,0≤Ф≤π)为偶函数图像上相邻的两个最高点之间的距离为2π.
(1)求f(x)的解析式
(2)若α∈(-π/3,π/2),且f(α+π/3)=1/3,求sin(2α+5π/3)的值
已知函数f(x)=sin(wx+Ф)(w>0,0≤Ф≤π)为偶函数图像上相邻的两个最高点之间的距离为2π.(1)求f(x)的解析式(2)若α∈(-π/3,π/2),且f(α+π/3)=1/3,求sin(2α+5π/3)的值
1、条件说明周期为2π,则w=1.
又因为f(x)为R上偶函数,且0≤Ф≤π,所以Ф=π/2
f(x)=sin(x+π/2)
2、α+π/3+π/2∈(π/2,4π/3) 所以cos(α+5π/6)
(1)T/2=2π,w=1/2
sin(wx+Ф)=sin(-wx+Ф)=-sin(wx-Ф)=sin(wx-Ф+π)
所以有wx+Ф=wx-Ф+π
所以Ф=π/2
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