答案(-3,0]

8.作出函数y=sin x-2在[0,2π]上的图像.

解列表.

x 0 π/2 π 3π/2 2π sin x 0 1 0 -1 0 sin x-2 -2 -1 -2 -3 -2

　　描点,用光滑的曲线顺次连接各点,可得y=sin x-2(x∈[0,2π])的图像(如图所示).

9.利用正弦函数的图像,求满足下列关系的角x的值或范围.

(1)1-2sin x=0;(2)√3/2+sin x≤0.

解(1)方程化为sin x=1/2,在[0,2π)内,方程sin x=1/2的解为π/6 或 5π/6.故所求的角x的集合为{x├|x=π/6+2kπ┤┤或x=├ 5π/6+2kπ"," k"∈" Z}.

　　(2)不等式化为sin x≤-√3/2,在[0,2π)内满足不等式的角x的集合为4π/3≤x≤5π/3.故所求的角x的集合为{x├|2kπ+4π/3≤x≤2kπ+5π/3 "," k"∈" Z}┤.

10.导学号93774017方程sin x=(1"-" a)/2在x∈[π/3 "," π]上有两个实数解,求a的取值范围.

解设y1=sin x,x∈[π/3 "," π],y2=(1"-" a)/2,y1=sin x,x∈[π/3 "," π]的图像如图.由图可知,当√3/2≤(1"-" a)/2<1,

即-1