将函数f(x)=sin^2x+sin2x+3cos^2x写成f(x)=Asin(wx+n)+k的形式_数学解答

将函数f(x)=sin^2x+sin2x+3cos^2x写成f(x)=Asin(wx+n)+k的形式

人气：228 ℃　时间：2019-08-20 02:43:35

解答

f(x)=sin^2x+sin2x+3cos^2x=sin^2x+2sinxcosx+3cos^2x=sin^2x+2sinxcosx+cos^2x+2cos^2x=1+sin2x+2cos^2x-1+1=sin2x+cos2x+2=√2(√2/2sin2x+√2/2cos2x)+2=√2(sin2xcosπ/4+cos2xsinπ/4)+2=√2sin(2x+π/4)+2...