Question

数学题( •̥́ ㉨ •̀ू )嘤嘤嘤~

数学题( •̥́ ㉨ •̀ू )嘤嘤嘤~来两道提刷刷脑

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Answer 1

①2kπ - π/2≤2x - π/4≤2kπ + π/2
2kπ - π/4≤2x≤2kπ + 3π/4
kπ - π/8≤x≤kπ + 3π/8，(k∈Z)
②T=2π/2=π
③∵正弦函数的值域是[-1，1]
∴y的最大值是2，
此时2x - π/4=2kπ + π/2
2x=2kπ + 3π/4
则x=2kπ + 3π/8，k∈Z
y的最小值是-2
此时2x - π/4=2kπ - π/2
2x=2kπ - π/4
则x=kπ - π/8，k∈Z
④∵π/4≤x≤π/2
∴π/2≤2x≤π
则π/4≤2x - π/4≤3π/4
∴√2≤y≤1

追答

2、y=3sin[-(2x - π/3]
=-3sin(2x - π/3)
①2kπ + π/2≤2x - π/3≤2kπ + 3π/2
2kπ + 5π/6≤2x≤2kπ + 11π/6
kπ + 5π/12≤x≤kπ + 11π/12，k∈Z
②∵0≤x≤π/2
∴0≤2x≤π
则-π/3≤2x - π/3≤2π/3
∴-3≤y≤(3√3)/2

Answer 2

题目不全