f(x)=3sin^2x+2（根3）sinxcosx+cos^2x求函数f(x)最大值与单调增区间

f(x)=3sin^2x+2（根3）sinxcosx+cos^2x求函数f(x)最大值与单调增区间
f(x)=3sin^2x+2（根3）sinxcosx+cos^2x求函数f(x)最大值与单调增区间

f(x)=3sin^2x+2（根3）sinxcosx+cos^2x求函数f(x)最大值与单调增区间
f(x)=3sin^2x+2根号3sinxcosx+cos^2x
=2sin^2x+√3sin2x+(cos^2x+sin^2x)
=(1-cos2x)+根号3sin2x+1
=2(sin2x*cos30-sin30cos2x)+2
=2sin(2x-30)+2
函数的最大值是:2*1+2=4
单调增区间是:2KPai-Pai/2

f(x)=3sin^2x+2根号3sinxcosx+cos^2x
=2sin^2x+√3sin2x+(cos^2x+sin^2x)
=(1-cos2x)+根号3sin2x+1
=2(sin2x*cos30-sin30cos2x)+2
=2sin(2x-30)+2
函数的最大值是:2*1+2=4
单调增区间是:2KPai-Pai/2<=2x-Pai/6<=2kPai+Pai/2
即是[kPai-Pai/6,kPai+Pai/3]