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