y=sin(2x+π/6),x属于[π/6,3π/4],求值域

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/03 08:10:29
y=sin(2x+π/6),x属于[π/6,3π/4],求值域

y=sin(2x+π/6),x属于[π/6,3π/4],求值域
y=sin(2x+π/6),x属于[π/6,3π/4],求值域

y=sin(2x+π/6),x属于[π/6,3π/4],求值域
π/6<=x<=3π/4
π/3<=2x<=3π/2
π/2<=2x+π/6<=5π/3
π/2<=x<=3π/2
sinx是减函数
所以sin(3π/2)<=sin(2x+π/6)<=sin(π/2)
-1<=sin(2x+π/6)<=1
而sin(2x+π/6)值域本身就是[-1,1]
所以3π/2<=2x+π/6<=5π/3肯定也属于[-1,1]
所以值域[-1,1]