已知函数f(x)=(six+cost)的平方＋2cost的平方，求函数f(x)的最小正周期及函数f(x)的最大值

显示全部楼层 · 2012-7-8 10:36:34

f(x)=(sinx+cosx)2＋2cos2x=1+2sinxcosx+cos2x+1=sin2x+cos2x+2=√2sin(2x+π/4)+2，f(x)的最小正周期T=2π/2=π，f(x)的最大值是2+√2。...

千问 · 2012-7-8 10:36:34

f(t)=(sint+cost)^2＋2(cost)^2=1+2sintcost+2(cost)^2=1+sin(2t)+cos(2t)+1=2+sin(2t)+cos(2t)=√2sin(2t+45°)+2T=2π/2=πsin(2t+45°)最大值为1，f(x)MAX=√2+2...

千问 · 2012-7-8 10:36:34

y=1+sin2t+(1+cos2t)= sin2t+cos2t+2=√2sin(2t+π/4)+2最小正周期T=2π /2=π当2t+π/4=π/2+2kπ即t=π/8+kπ时，y取最大值，y(MAX)=√2+2...