Question

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

Answer 1

【答案】分析：通過誘導公式sin89°=cos1°，得出sin²1°+cos²1°=1，依此類推，得出原式=44×1+sin²45°，得出答案．
解答：解：∵sin89°=cos（90°-1°）=cos1°
∴sin²1°+sin²89°=sin²1°+cos²1°=1
同理sin2°+sin88°=1，…sin44°+sin46°=1
∴sin²1°+sin²2°+sin²3°+…+sin²88°+sin²89°=44+=44.5
故答案為44.5．
點評：分析本題主要考查了三角函數中的誘導公式的運用．屬基礎題．