化简:sin(-870°)cos930°+cos(-1380°)sin(-690°)+tan585°

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化简:sin(-870°)cos930°+cos(-1380°)sin(-690°)+tan585°

化简:sin(-870°)cos930°+cos(-1380°)sin(-690°)+tan585°
化简:sin(-870°)cos930°+cos(-1380°)sin(-690°)+tan585°

化简:sin(-870°)cos930°+cos(-1380°)sin(-690°)+tan585°
sin(-870°)cos930°+cos(-1380°)sin(-690°)+tan585°
=sin(-870°+1080°)cos(1080-150°)+cos(-1380°+1440°)sin(-690°+720°)+tan(720°-135°)
=sin(210°)cos150°+cos60°sin30°-tan135°
=sin(180°+30°)cos(180°-30°)+cos60°sin30°-tan(180°-45°)
=sin30°cos30°+cos60°sin30°+tan45°
=sin30°cos30°+cos60°sin30°+tan45°
=1/2*√3/2+1/2*1/2+1
=√3/4+2

sin(-870°)cos930°+cos(-1380°)sin(-690°)+tan585°
=-sin30°*(-cos30°)+cos60°*sin30°+tan45°
=√3/4+√3/4+1
=(2+√3)2

sin(-870°)cos930°+cos(-1380°)sin(-690°)+tan585°
=sin(-150°-2*360°)cos(3*360°-150°)+cos(-4*360°+60°)sin(-2*360°+30°)+tan(2*360°-135°)
=sin(-150°) * cos(-150°)+cos(60°)sin(30°)+tan(-135°)
=(-1/2)*(-√3/2)+1/2 *1/2 -(-1)=5/4+√3/4

sin(-870°)cos930°+cos(-1380°)sin(-690°)+tan585°
=sin(180°+30°)cos(180°-30°)+cos60°sin30°-tan(180°-45°)
=-sin30°*(-cos30°)+cos60°*sin30°+tan45°
=√3/4+√3/4+1
=(2+√3)2