一道数学题:sim²1°+sim²2°+sim²3°+…+sim²89° 的结果多少,给出过程最好
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/22 05:30:42
![一道数学题:sim²1°+sim²2°+sim²3°+…+sim²89° 的结果多少,给出过程最好](/uploads/image/z/764427-3-7.jpg?t=%E4%B8%80%E9%81%93%E6%95%B0%E5%AD%A6%E9%A2%98%EF%BC%9Asim%26%23178%3B1%C2%B0%2Bsim%26%23178%3B2%C2%B0%2Bsim%26%23178%3B3%C2%B0%2B%E2%80%A6%2Bsim%26%23178%3B89%C2%B0+%E7%9A%84%E7%BB%93%E6%9E%9C%E5%A4%9A%E5%B0%91%2C%E7%BB%99%E5%87%BA%E8%BF%87%E7%A8%8B%E6%9C%80%E5%A5%BD)
一道数学题:sim²1°+sim²2°+sim²3°+…+sim²89° 的结果多少,给出过程最好
一道数学题:sim²1°+sim²2°+sim²3°+…+sim²89° 的结果多少,给出过程最好
一道数学题:sim²1°+sim²2°+sim²3°+…+sim²89° 的结果多少,给出过程最好
能帮到你很好
sin²1°+sin²2°+sin²3°+…+sin²89°
=(sin²1°+sin²89°)+(sin²2°+sin²88°)+……+(sin²44°+sin²46°)+sin²45°
=(cos²89°+sin²89°)+(cos²88°+sin²88°)+……+(cos²46°+sin²46°)+sin²45°
=1+1+……+1+1/2
=44+1/2
=89/2
如果A+B=90°
那么sinB=sin(90°-A)=cosA
所以(sinA)^2+(sinB)^2=(sinA)^2+(cosA)^2=1
那么(sin1°)^2+(sin89°)^2=1
(sin2°)^2+(sin88°)^2=1
..........
(sin44°)^2+(sin46°)^2=1
(sin45°)^2=1/2
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如果A+B=90°
那么sinB=sin(90°-A)=cosA
所以(sinA)^2+(sinB)^2=(sinA)^2+(cosA)^2=1
那么(sin1°)^2+(sin89°)^2=1
(sin2°)^2+(sin88°)^2=1
..........
(sin44°)^2+(sin46°)^2=1
(sin45°)^2=1/2
所以,原式=[(sin1°)^2+(sin89°)^2]+[(sin2°)^2+(sin88°)^2]+.....[(sin44°)^2+(sin46°)^2]+(sin45°)^2
=1x44+1/2=89/2
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解sin²1°+sin²2°+sin²3°+…+sin²89°
=(sin²1°+sin²89°)+(sin²2°+sin²88°)+…+(sin²44°+sin²46°)+sin²45°
=(sin²1°+cos²1°)+(sin²2°+cos²2°)+…+(sin²44°+cos²44°)+sin²45°
=1×44+(√2/2)^2
=44+1/2
=89/2
sinθ=cos(90°-θ)
所以sin²1°+sin²2°+sin²3°+…+sin²89°
=(sin²1°+cos²1°)+(sin²2°+cos²2°)+...+(sin²44°+cos²44°)+sin²45°
=1+1+...+1+1/2
=89/2
如果不懂,请追问,祝学习愉快!
是sin吧!
令s=sin²1°+sin²2°+sin²3°…+sin²89° ..(1)
则s=sin²89°+sin²88°+sin²87°…sin²1°
=cos²1°+cos²2°+cos²3°...+cos²89° ..(2)
(1)+(2),得2s=1+1+...+1
2s=89*1
s=89/2