Question

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

解：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