化简f(x)=2(sinx)^2+sinxcosx+(cosx)^2

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/03 18:54:23
化简f(x)=2(sinx)^2+sinxcosx+(cosx)^2

化简f(x)=2(sinx)^2+sinxcosx+(cosx)^2
化简f(x)=2(sinx)^2+sinxcosx+(cosx)^2

化简f(x)=2(sinx)^2+sinxcosx+(cosx)^2
f(x)=2(sinx)^2+sinxcosx+(cosx)^2
=sinx^2+sinxcosx+1
=1/2 (1-cos2x)+1/2sin2x+1
=1/2(sin2x-cos2x)+3/2
=√2/2(√2/2sin2x-√2/2cos2x)+3/2
=√2/2(sin2xcosπ/4-cos2xcosπ/4)+3/2
=√2/2sin(2x-π/4)+3/2

貌似简单,忘了 - -

f(x)=(sinx)^2+1/2*sin2x+1
=1/2-1/2cos2x+1/2*sin2x+1
=3/2+sin(2x-60°)