sin3x-sin2x+sinx=0

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/19 12:41:47
sin3x-sin2x+sinx=0
x)+3F@&H~ ~`-Єs*+QHDITS64FFw=}ѽSxvɳ*l7 <\`yo=2F@VhB z>{ӽ{ik]=,|6mFqF`gXٌ/Y Vlӎ%O;V?hf[C] <;P2

sin3x-sin2x+sinx=0
sin3x-sin2x+sinx=0

sin3x-sin2x+sinx=0
sin3x
=sin(2x+x)
=sin2xcosx+cos2xsinx
=2sinxcosxcosx+cos2xsinx
=2sinxcos²x+cos2xsinx
sin3x-sin2x+sinx
=2sinxcos²x+cos2xsinx-sin2x+sinx=0
若sinx=0 此时x=kπ
若sinx≠0时,得:
2cos^2x+cosx+1=0
相当于一元二次方程2x^2+x+1=0的解
易知此方程无解(判别式△=1-8