Question

已知函数f(x)=Asin(wx-π/3)(A＞0,w＞0)在某一个时期内的图像的最高点和最低点的坐标分别为(5π/12

Answer 1

显然A=2；由最高点和最低点坐标得：w*(5π/12)-π/3=2kπ+π/2； w*(11π/12)-π/3=2kπ+3π/2

由此解得w=2.

因为f(b)=2sin(2b-π/3)=2[sin(2b)*cos(π/3) - cos(2b)*sin(π/3) ] =sin(2b) - 3^(0.5)*cos(2b)

又sin(2b) = 2sin(b)*cos(b) cos(2b) = 1-2(sinb)^2;

由sin(b)^2 + cos(b)^2 =1 ,得 cos(b) = 3/5

带入得 f(b)= 24/25 - (7/25)* (3^(0.5))