高一数学与y=Asin(wx+&)有关的题若函数f(x)的定义域为R,最小正周期为3π/2,且满足f(x)=①cosx,-π/2≤x<0,②sinx,0≤x<π,则f(-15π/4)

问题描述:

高一数学与y=Asin(wx+&)有关的题
若函数f(x)的定义域为R,最小正周期为3π/2,且满足f(x)=①cosx,-π/2≤x<0,②sinx,0≤x<π,则f(-15π/4)

由于f(x)的周期为3π/2,所以f(-15π/4)=f(-15π/4+3×3π/2)=f(3π/4).又f(x)=①cosx,-π/2≤x<0,②sinx,0≤x<π,所以f(3π/4)=sin(3π/4)=√2/2