Question

已知函数f(x)=2cos2x+(sinx)^2-4cosx

已知函数f(x)=2cos2x+(sinx)^2-4cosx.(1)求f(π/3)的值；（2）求f(x)的最大值和最小值

Answer 1

(1) f(x)=2cos2x+sinx^2
=2(1-2sinx^2)+sinx^2
=-3sinx^2+2
f(π/3)=-3[sin(π/3)]^2+2
=-3x3/4+2
=-1/4
(2)求f(x)的最大值和最小值。
易知当sinx=0时有最大值为，2
当sinx=1或-1时有最小值为，-1 请采纳谢谢

Answer 2

f(x) = sin(x/2)cos(x/2) cos�0�5(x/2) - 1/2
= (1/2)sinx (1/2)cosx 1/2 - 1/2
= (1/2)(sinx cosx)
= (1/2)×√2×sin(x ψ) 【ψ = arctan(b/a)】
= √2/2sin(x ψ)
周期 T = 2π/1 = 2π