函数f(x)=cos2x+2sinx(x属于R)的最大值是

显示全部楼层 · 2011-9-17 11:35:35

f(x)=cos2x+2sinx
=1-sin2x+2sinx
=-(sin2x-2sinx+1-1)+1
=-(sinx-1)2+2当sinx=1时，f(x)有最大值2...

千问 · 2011-9-17 11:35:35

f(x)=cos2x+2sinx =1-2sin^2+2sinx=-2(sin^2+sinx)+1=-2(sin^2+sinx+1/4-1/4)+1
配方求最大值=-2（sinx+1/2)^2+1+1/2=3/2-2(sinx+1/2)^2sinx∈[-1,1]
要使f(x)娶最大值，则-2(sinx+1/2...

千问 · 2011-9-17 11:35:35

f(x)=cos2x/5 sin2x/5 =根号2 sin(2x/5 π/4) 最大值是:根号2.(1是错的) 周期T=2π/(2/5)=5π。（2是错的）相邻的两条对称轴之间的...