Question

已知函数f（x）=sin（2x-A）+1满足f（（π/3）+x)=f（（π/3）-x),则A等于多少?

Answer 1

令x=π/3 代入f（（π/3）+x)=f（（π/3）-x)

f(0)=sinA+1=f(2π/3)=sin((4π/3)-A）+1

sinA=sin((4π/3)-A）=sin(4π/3)cosA-cos(4π/3)sinA/2((1-sinA)^0.5=-3^0.5/2((1-(sinA)^2)^0.5)+0.5sinA

移项得0.5sinA=-3^0.5((1-(sinA)^2)^0.5)

(此处见sinA为负)

两边平方得0.25(sinA)^2=0.75(1-(sinA)^2)

(sinA)^2=3／4

开方得A=2kπ-π/3 A=2kπ+4π/3