f(x)=cos(3x+90°)(x∈R)1.最小正周期?2.f(x)是奇函数?3.关于(6O°,0)对称?4.在[0,6O°]是减函数?
题目
f(x)=cos(3x+90°)(x∈R)1.最小正周期?2.f(x)是奇函数?3.关于(6O°,0)对称?4.在[0,6O°]是减函数?
答案
最小正周期是2π/3
f(x)=cos(3x+90°)=-sin3x
f(-x)=sin3x=-f(x)
是奇函数
3)对称点是3x=kπ x=kπ/3
所以关于(60°,0)对称,此时k=1
4)单调减区间是1/3*(2kπ-π/2,2kπ+π/2)
所以不是单调减
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