函数f(x)=√3cos2/5x+sin2/5x的图像相邻的两条对称轴之间的距离是----
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![函数f(x)=√3cos2/5x+sin2/5x的图像相邻的两条对称轴之间的距离是----](/uploads/image/z/1618288-16-8.jpg?t=%E5%87%BD%E6%95%B0f%28x%29%3D%E2%88%9A3cos2%2F5x%2Bsin2%2F5x%E7%9A%84%E5%9B%BE%E5%83%8F%E7%9B%B8%E9%82%BB%E7%9A%84%E4%B8%A4%E6%9D%A1%E5%AF%B9%E7%A7%B0%E8%BD%B4%E4%B9%8B%E9%97%B4%E7%9A%84%E8%B7%9D%E7%A6%BB%E6%98%AF----)
函数f(x)=√3cos2/5x+sin2/5x的图像相邻的两条对称轴之间的距离是----
函数f(x)=√3cos2/5x+sin2/5x的图像相邻的两条对称轴之间的距离是----
函数f(x)=√3cos2/5x+sin2/5x的图像相邻的两条对称轴之间的距离是----
f(x)=√3cos(2x/5)+sin(2x/5)
=2[√3cos(2x/5)/2+sin(2x/5)/2]
=2[sin(π/3)cos(2x/5)+cos(π/3)sin(2x/5)]
=2sin(2x/5+π/3)
f(x)的周期为2π/(2/5)=5π
2sin(2x/5+π/3)的对称轴之间的距离即为f(x)的半周期
f(x)两条对称轴之间的距离是5π/2
或者这样解
当2x/5+π/3=π/2时,x=5π/12
当2x/5+π/3=-π/2时,x=-25π/12
5π/12-(-25π/12)=5π/2
f(x)两条对称轴之间的距离是5π/2
解:(圆周率Pi)
f(x)=2(√3/2*cos2/5x+1/2*sin2/5x)
=2sin(2/5x+Pi/3)
令2/5*x+Pi/3=Pi/2+k*Pi(k属于整数)
x=5/12*Pi+5/2*k*Pi(k属于整数)
所以对阵轴为直线x=5/12*Pi+5/2*k*Pi(k属于整数)
所以图像相邻的两条对称轴之间的距离
d...
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解:(圆周率Pi)
f(x)=2(√3/2*cos2/5x+1/2*sin2/5x)
=2sin(2/5x+Pi/3)
令2/5*x+Pi/3=Pi/2+k*Pi(k属于整数)
x=5/12*Pi+5/2*k*Pi(k属于整数)
所以对阵轴为直线x=5/12*Pi+5/2*k*Pi(k属于整数)
所以图像相邻的两条对称轴之间的距离
d=(5/12*Pi+5/2*k*Pi)-[5/12*Pi+5/2*(k-1)*Pi]
=[5/2*k-5/2*(k-1)]*Pi
=5/2*Pi
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