求sin21°+sin22°+sin23°+…+sin288°+sin289°的值_．

分类: 作业答案 • 2022-01-09 18:03:45

问题描述：

求sin²1°+sin²2°+sin²3°+…+sin²88°+sin²89°的值______．

答

∵sin89°=sin（90°-1°）=cos1°
∴sin²1°+sin²89°=sin²1°+cos²1°=1
同理sin2°+sin88°=1，…sin44°+sin46°=1
∴sin²1°+sin²2°+sin²3°+…+sin²88°+sin²89°=44+

=44.5
故答案为44.5．