利用单位圆中的三角函数线,求满足下列条件的x的集合 (1)sinx≤根号2⼀2 (2)cosx≥-1⼀2,且sinx≥根号3⼀2

2025-04-13 23:28:54
推荐回答(2个)
回答1:

1)sinx≤根号2/2, 解得{x│2kπ-5π/4≤x≤2kπ+π/4,k∈Z}
2)cosx≥-1/2 解得{x│2kπ-2π/3≤x≤2kπ+2π/3, k∈Z}
sinx≥根号3/2 解得{x│2kπ+π/3≤x≤2kπ+2π/3, k∈Z}
则{x│2kπ-2π/3≤x≤2kπ+2π/3, k∈Z}∪{x│2kπ+π/3≤x≤2kπ+2π/3, k∈Z}
={x│2kπ+π/3≤x≤2kπ+2π/3, k∈Z}

回答2:

(1){x|-5π/4+2kπ≤x≤π/4+2kπ,k∈Z};
(2){x|π/3+2kπ≤x≤2π/3+2kπ,k∈Z}。