函数y=2sin(π6-2x),x∈[π6,π2]的值域为______.-数学

题目简介

函数y=2sin(π6-2x),x∈[π6,π2]的值域为______.-数学

题目详情

函数y=2sin(
π
6
-2x
),x∈[
π
6
π
2
]的值域为______.
题型:填空题难度:中档来源:不详

答案

当x∈[class="stub"π
6
,class="stub"π
2
]时,class="stub"π
6
-2x
∈[-class="stub"5π
6
,-class="stub"π
6
]
class="stub"π
6
-2x
=-class="stub"π
6
或-class="stub"5π
6
时,即x=class="stub"π
6
class="stub"π
2
时,函数y=2sin(class="stub"π
6
-2x
)取最大值-1;
class="stub"π
6
-2x
=-class="stub"π
2
时,x=class="stub"π
3
时,函数y=2sin(class="stub"π
6
-2x
)取最小值-2;
则函数y=2sin(class="stub"π
6
-2x
)的值域为[-2,-1]
故答案为:[-2,-1]

更多内容推荐