三道关于高一三角函数的题目

来源：百度知道 编辑：UC知道 时间：2024/06/21 11:59:25
1)求值cos(π/5)cos(2π/5)

2)求函数y=1-(cosx)^2+(cosx)^4的最小正周期

3)求函数y=2sinx(sinx+cosx)的减区间

答案:1)0.25 2)π/4 3)[kπ+3/8π,kπ+7/8π]

1)1/4
∵cos(π/5)cos(2π/5)+sin(π/5)sin(2π/5)=cos(π/5)
cos(π/5)cos(2π/5)-sin(π/5)sin(2π/5)=cos(3π/5)
∴cos(π/5)cos(2π/5)=[cos(π/5)+cos(3π/5) ]/2
又∵cos(π/5)+cos(3π/5)=cos(π/5)-cos(2π/5)
cos(π/5)-cos(2π/5)=-cos(4π/5)-cos(2π/5)
cos(π/5)-2cos(π/5)^2+1=-cos(2π/5)-2cos(2π/5)^2+1
cos(π/5)-2cos(π/5)^2=-cos(2π/5)-2cos(2π/5)^2
cos(π/5)+cos(2π/5)=[cos(π/5)^2-cos(2π/5)^2]*2
[cos(π/5)-cos(2π/5)]*2=1
∴cos(π/5)cos(2π/5)=[cos(π/5)+cos(3π/5) ]/2=1/4

2）y=1-(cosx)^2+(cosx)^4
=1+(cosx)^2*[(cosx)^2-1]
=1+(sin2x)^2/4

3）y=2*(sinx)^2+sin2x
=1-cos2x+sin2x
=1- (根号2)*sin(x-π/4)

汗~~~，这也问