cos1°+cos2°+cos3°+.+cos359°等于多少.

分类: 作业答案 • 2021-12-20 01:40:48

问题描述：

答

0
cos1+cos2+...+cos90与cos271+cos272+...+cos359相消为0
cos91+cos92+...+cos180与cos181+cos182+...+cos270相消为0

答

因cos(x)+cos(x+PI)=＝cos(x)+cos(x)cos(PI)-sin(x)sin(PI)=0;
所以原式＝0

答

cos1°=cos359° cos2°=cos358°
原题化为(cos1°+cos2°+...cos179°)*2+cos180°
cos1°+cos179°=0
cos2°+cos178°=0
cos90°=0
所以答案是1

答

cosx + cos(pi+x) = cosx - cosx = 0;
原式 = (cos1 + cos 181) + ... + (cos179 + cos359) + cos180
= cos180 = -1.