已知函数f(x)=2sinx(sinx+cosx)-1,在平面直角坐标系中画出函数f(x)在【0,180】

题目

已知函数f(x)=2sinx(sinx+cosx)-1,在平面直角坐标系中画出函数f(x)在【0,180】

答案

f(x)=2sinx(sinx+cosx)-1
=2sinx*sinx+2sinx*cosx-(sinx*sinx-cosx*cosx)
=sinx*sinx-cosx*cosx+2sinx*cosx
=-cos2x+sin2x
=sin2x-cos2x
=√2((sin2x*(1/√2)-cos2x*(1/√2)))
=√2((sin2x*cos(π/4)-cos2x*sin(π/4)))
=√2((sin(2x-π/4))