已知f(x)=sin(2x+π/3)+sin(2x-π/3),g(x)=(√3)cos2x若一动点直线x=t与函数y=f(x),y=g(x)的图像分别交于M、N两点,求|MN|的最大值
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![已知f(x)=sin(2x+π/3)+sin(2x-π/3),g(x)=(√3)cos2x若一动点直线x=t与函数y=f(x),y=g(x)的图像分别交于M、N两点,求|MN|的最大值](/uploads/image/z/2739000-48-0.jpg?t=%E5%B7%B2%E7%9F%A5f%28x%29%3Dsin%282x%2B%CF%80%2F3%29%2Bsin%282x-%CF%80%2F3%29%2Cg%28x%29%3D%EF%BC%88%E2%88%9A3%EF%BC%89cos2x%E8%8B%A5%E4%B8%80%E5%8A%A8%E7%82%B9%E7%9B%B4%E7%BA%BFx%3Dt%E4%B8%8E%E5%87%BD%E6%95%B0y%3Df%28x%29%2Cy%3Dg%28x%29%E7%9A%84%E5%9B%BE%E5%83%8F%E5%88%86%E5%88%AB%E4%BA%A4%E4%BA%8EM%E3%80%81N%E4%B8%A4%E7%82%B9%2C%E6%B1%82%7CMN%7C%E7%9A%84%E6%9C%80%E5%A4%A7%E5%80%BC)
已知f(x)=sin(2x+π/3)+sin(2x-π/3),g(x)=(√3)cos2x若一动点直线x=t与函数y=f(x),y=g(x)的图像分别交于M、N两点,求|MN|的最大值
已知f(x)=sin(2x+π/3)+sin(2x-π/3),g(x)=(√3)cos2x
若一动点直线x=t与函数y=f(x),y=g(x)的图像分别交于M、N两点,求|MN|的最大值
已知f(x)=sin(2x+π/3)+sin(2x-π/3),g(x)=(√3)cos2x若一动点直线x=t与函数y=f(x),y=g(x)的图像分别交于M、N两点,求|MN|的最大值
f(x)=sin(2x+π/3)+sin(2x-π/3),g(x)=(√3)cos2x
一动点直线x=t与函数y=f(x),y=g(x)的图像分别交于M、N两点
f(x)-g(x)
=sin(2x+π/3)+sin(2x-π/3)-√3cos2x
=sin2xcosπ/3+cos2xsinπ/3+sin2xcosπ/3-cos2xsinπ/3 -√3cos2x
=2sin2x*1/2-√3cos2x
=sin2x-√3cos2x
=2(1/2sin2x-√3/2cos2x)
=2sin(2x-π/3)
∴|MN|=2|sin(2t-π/3)|
2t-π/3=π/2+2kπ,k∈Z时, |MN|取得最大值为2