已知:函数f(x)=2cos2x+sin^2x已知:函数f(x)=2cos2x+sin^2x..(1)求f(派/3)的值(2)求f(x)的最大值和最小值...小弟真没分了..

Question

已知 :函数 f ( x )= 2cos2x+sin^2x
已知 :函数 f ( x )= 2cos2x+sin^2x..(1)求f(派/3)的值
(2)求f(x)的最大值和最小值...小弟真没分了..

Answer 1

(1)
f(π/3)=2cos[2·(π/3)]+sin²(π/3)
=2cos(2π/3) +sin²(π/3)
=2·(-1/2)+(√3/2)²
=-1+3/4
=-1/4
(2)
f(x)=2cos(2x)+sin²x
=2(1-2sin²x)+sin²x
=-3sin²x+2
-1≤sinx≤1
0≤sin²x≤1
sin²x=0时,f(x)有最大值f(x) max=2
sin²x=1时,f(x)有最小值f(x) min=-1