函数y=根号3sinxcosx+cos^2x-1/2在[0,π/2]的值域是?A.[-1,1]B.[1/2,1]C.[0,1]D._数学解答

函数y=根号3sinxcosx+cos^2x-1/2在[0,π/2]的值域是?
A.[-1,1]
B.[1/2,1]
C.[0,1]
D.[-1/2,1]
根号3

人气：159 ℃　时间：2019-12-09 10:05:29

解答

y=√3sinxcosx+cos^2x-1/2 =（√3/2）sin2x+（1/2）（cos2x+1）-1/2 =（√3/2）sin2x+（1/2）cos2x =sin（2x+π/6）因为x属于[0,π/2],所以2x+π/6属于[π/6,7π/6] 所以最小值为sin（7π/6）=-0....