设函数f(x)=3sin(wx+TT/6),w>0,x∈(负无穷,正无穷),且以TT/2为最小正周期,求f(0)设函数f(x)=3sin(wx+TT/6),w>0,x∈(负无穷,正无穷),且以TT/2为最小正周期,求(1)f(0);(2)求f(x)解释式;(3)已知f(a/4+TT/12)=9/5,求sina的值

问题描述:

设函数f(x)=3sin(wx+TT/6),w>0,x∈(负无穷,正无穷),且以TT/2为最小正周期,求f(0)
设函数f(x)=3sin(wx+TT/6),w>0,x∈(负无穷,正无穷),且以TT/2为最小正周期,求(1)f(0);(2)求f(x)解释式;(3)已知f(a/4+TT/12)=9/5,求sina的值

(1)
f(0)=3sin(w*0+π/6)=3sinπ/6=3/2;
(2)
f(x)=3sin(wx+π/6)的最小周期为:2π/w
又由题意知π/2为最小正周期;
∴2π/w=π/2,w=4
∴f(x)=3sin(4x+π/6)
(3)
f(a/4+π/12)=3sin[4*(a/4+π/12)+π/6]
=3sin(a+π/2)
=3cosa
又f(a/4+TT/12)=9/5
∴3cosa=9/5
cosa=3/5;
∴sina=±√(1-cosa²)=±4/5;