(sin1度)^2+(sin2度)^2+…+(sin89度)^2+(sin90度)^2的值
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![(sin1度)^2+(sin2度)^2+…+(sin89度)^2+(sin90度)^2的值](/uploads/image/z/2563265-65-5.jpg?t=%28sin1%E5%BA%A6%29%5E2%2B%28sin2%E5%BA%A6%29%5E2%2B%E2%80%A6%EF%BC%8B%28sin89%E5%BA%A6%29%5E2%EF%BC%8B%28sin90%E5%BA%A6%29%5E2%E7%9A%84%E5%80%BC)
(sin1度)^2+(sin2度)^2+…+(sin89度)^2+(sin90度)^2的值
(sin1度)^2+(sin2度)^2+…+(sin89度)^2+(sin90度)^2的值
(sin1度)^2+(sin2度)^2+…+(sin89度)^2+(sin90度)^2的值
S=(sin1度)^2+(sin2度)^2+…+(sin89度)^2+(sin90度)^2
S=(sin0度)^2+(sin1度)^2+(sin2度)^2+…+(sin89度)^2+(sin90度)^2 (1)
倒序写一下
S=(sin90度)^2+(sin89度)^2+(sin88度)^2+…+(sin1度)^2+(sin0度)^2
所以
S=(cos0度)^2+(cos2度)^2+(cos3度)^2+…+(cos1度)^2+(cos0度)^2 (2)
(1)+(2)
2S=91
S=45.5
(sin1度)^2+(sin2度)^2+…+(sin89度)^2+(sin90度)^2
=[(sin1度)^2+(sin89度)^2]+[(sin2度)^2+(sin88度)^2]+…+[(sin44度)^2+(sin46度)^2]
+(sin45度)^2+(sin90度)^2
=[(sin1度)^2+(cos1度)^2]+[(sin2度)^2+(cos2度)^2]+…+[(sin44度)^2+(cos44度)^2]+1/2+1
=1+1+1+......+1+1/2+1
=44+1/2+1
=91/2
44.5
因为sin(90度-X)的平方=COS(X)的平方。
而sinX度的平方+COS(X)度的平方=1
其中以 45度,分界,左右头加尾共得44,而sin45度的平方=0。5
有44+0.5=44.5