求函数f(x)=1/2sin方α+cos方α+根号3/4sin2α最大值最小值

显示全部楼层 · 2013-2-10 19:11:31

f(x)=1/2*(sin2x+cos2x)+1/2*cos2x+√3/4*sin2x=1/2+1/2*(1+cos2x)/2+√3/4*sin2x=3/4+1/2*(sin2x*√3/2+cos2x*1/2)=3/4+1/2*sin(2x+π/3)则sin)2x+π/3)=±1是最值所以{x|x=kπ-5π/12},最小值是1/4{x|x=kπ+π/12},最大值是5/4...

千问 · 2013-2-10 19:11:31

f(α)=1/2sin方α+cos方α+根号3/4sin2α
=（1/2sin方α+cos方α+根号3/2sinαcosα）/(sin方α+cos方α)
=（tan方α+（根号3）tanα+2）/(2tan方α+2tanα)
=1/2+(（根号3）tanα+1）/(2tan方α+2tanα)f(α)=(（根号3）tan...