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Rsina=R-b/2,
Rsina=b-Rcosa
b已知,求R和sina(要过程,或思想方法)
人气:157 ℃ 时间:2020-10-01 23:37:35
解答
Rsina=R-b/2(1)
Rsina=b-Rcosa(2)
(1)代入(2)
R-b/2=b-Rcosa
Rcosa=3b/2-R(3)
(1)²+(2)²
R²=(R-b/2)²+(3b/2-R)²
R²=R²-bR+b²/4+9b²/4-3bR+R²
R²-4bR+5b²/2=0
2R²-8bR+5b²=0
R=(8b±2√6b)/4=(4±√6)b/2
由(1)
sina=1-b/(2R)=1-1/(4±√6)
所以
R=(4+√6)b/2,sina=(6+√6)/10
R=(4-√6)b/2,sina=(6-√6)/10
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