求数学学霸为学渣我解决一道数学题 如下图

2025-04-27 11:42:33
推荐回答(2个)
回答1:

(1)
f(x)=sin(x+π/6)+sin(x-π/6)-cos2x+m (积化和差)
=2sinx·cosπ/6-cos2x+m (和差角公式、消项)
=2sin²x+√3sinx+m-1
=> t=2π

(2)
x∈[-π/4,π/4]
=> sinx∈[-√2/2,√2/2]
以sinx为自变量的抛物线的对称轴横坐标为-√3/4∈[-√2/2,√2/2],于是
2×(-√3/4)²+√3(-√3/4)+m-1=-3
解得m=-13/8

回答2: