a-maths!!!!!!!

2008-03-01 12:42 am
解下列方程,其中0≤x≤2π。答案以π表示。


3(secx+cotx)=13

回答 (1)

2008-03-01 6:53 am
✔ 最佳答案
沒有準確值的答案, 可以用牛頓法計算出大概值如下:
考慮 f(x) = 3(sec x + cot x) - 13, 則 f'(x) = 3(sec x tan x - csc2 x)
由 x0 = 1.5 開始計:
x1 = x0 - f(x0)/f'(x0) = 1.4502
x2 = x1 - f(x1)/f'(x1) = 1.3895
x3 = x2 - f(x2)/f'(x2) = 1.3417
x4 = x3 - f(x3)/f'(x3) = 1.3216
x5 = x4 - f(x4)/f'(x4) = 1.3247
x6 = x5 - f(x5)/f'(x5) = 1.3232
x7 = x6 - f(x6)/f'(x6) = 1.3232
即 0.421π
以相同手法, 在 0 ≦ x ≦ 2π 中能找到另一個答案為:
4.9336 = 1.570π
參考: My Maths knowledge


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