Question

在区间(0,π]上随机取一个数x,则事件"sinx+根号3cosx≤1"发生的概率是

答案是1/3求解啊

Answer 1

sinx+√3cosx
=2sin(x+π/3)<=1
sin(x+π/3)<=1/2
x+π/3∈(π/3,4π/3]
所以5π/6<=x+π/3<=4π/3
π/2<=x<=π
所以应该是(π-π/2)/(π-0)=1/2

追问

可是组长打了叉啊

追答

答案错了

追问

这么大整蛊

追答

采纳吧

Answer 2

sinx+根号3cosx
=2sin(x+π/3)<=1
sin(x+π/3)<=1/2
-7π/6+2kπ<=x+π/3<=π/6+2kπ （k∈Z）
解得
2kπ-3π/2<=x<=2kπ-π/6 在区间(0,π]上
k=1 π/2<=x<=π
在区间(0,π]上随机取一个数x,则事件"sinx+根号3cosx≤1"发生的概率是 1/2