(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

(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