作业帮sin(-480度)cos570度+cos(-300度)sin(-1050)急
来源：学生作业帮助网 编辑：作业帮 时间：2024/04/29 18:56:11
sin(-480度)cos570度+cos(-300度)sin(-1050)急
sin(-480度)cos570度+cos(-300度)sin(-1050)
急
sin(-480度)cos570度+cos(-300度)sin(-1050)急
sin(-480度)cos570度+cos(-300度)sin(-1050)
=-sin480°cos(360°+210°)+cos300°*(-sin1050°)
=-sin(360°+120°)cos210°-cos(360°-60°)sin(3*360°-30°)
=-sin120°cos(180°+30°)-cos60°(-sin30°)
=-sin(180°-60°)(-cos30°)+cos60°sin30°
=sin60°cos30°+cos60°sin30°
=sin(60°+30°)
=sin90°
=1
sin(-480度)cos570度+cos(-300度)sin(-1050)
=sin(-120)cos(150)+cos60sin30
=-sin60cos30+cos60sin30
=cos(60+30)
=cos90
=0
[1]
sin(-480)=-sin480=-sin(360+120)=-sin120=-sin60=-(√3)/2
cos570=cos(360+210)=cos210=cos(180+30)=-cos30=-(√3)/2
cos(-300)=cos300=cos(360-60)=cos60=1/2
sin(-1050)=-sin1050=-sin(3×360-30)=sin30=1/2
[2]
原式=(3/4)+(1/4)=1
sin(-480°)cos570°+cos(-300°)sin(-1050°)=sin[(-2)×360º+240°]cos(1×360°+210°)+cos[(-1)×360°+60°]sin[(-3)×360º+30º]=sin240°cos210°+cos60°sin30º=sin60º(-cos30º)+cos60ºsin30º=-sin60°cos30°+cos60°sin30°=sin(30°-60º)=sin(-30°)=-sin30º=-1/2.