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

题目简介

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

题目详情

求sin21°+sin22°+sin23°+…+sin288°+sin289°的值______.
题型:填空题难度:中档来源:不详

答案

∵sin89°=cos(90°-1°)=cos1°
∴sin21°+sin289°=sin21°+cos21°=1
同理sin2°+sin88°=1,…sin44°+sin46°=1
∴sin21°+sin22°+sin23°+…+sin288°+sin289°=44+class="stub"1
2
=44.5
故答案为44.5.

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