第六题的解题思路和过程
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由题意可知，sin（x)在[-π/2,π/2]内为增函数，在[π/2,3π/2]内为减函数。
-π/6<=X<=a
-3^0.5/2<=sin（X-π/6）<=1……1式
对于1式，分情况讨论：
1）当-π/2<=X-π/6<=π/2内，即x在[-π/3,2π/3]内
-π/3<=X-π/6<=π/2
解出：-π/6<=X<=2π/3
a（min）的取值为2π/3
2）当π/2<=X-π/6<=3π/2内，即x在[2π/3,5π/3]内
-π/3<=π-（X-π/6）<=π/2
解出2π/3<=X<=3π/2
-π/6<=X<=a
a（max）的取值为a=3π/2
综合上述
所以a的取值为2π/3<=a<=3π/2
-π/6<=X<=a
-3^0.5/2<=sin（X-π/6）<=1……1式
对于1式，分情况讨论：
1）当-π/2<=X-π/6<=π/2内，即x在[-π/3,2π/3]内
-π/3<=X-π/6<=π/2
解出：-π/6<=X<=2π/3
a（min）的取值为2π/3
2）当π/2<=X-π/6<=3π/2内，即x在[2π/3,5π/3]内
-π/3<=π-（X-π/6）<=π/2
解出2π/3<=X<=3π/2
-π/6<=X<=a
a（max）的取值为a=3π/2
综合上述
所以a的取值为2π/3<=a<=3π/2
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