急! 急! 急! F5 有關Solve數1條唔識 ?

原來你把同一道問題問了兩次，那麼我又可以回答了！首先樓上的方法是正確的，然而計錯了一個答案！而且如果題目沒有註明的話，還是建議取三個有效數字（比較方便、可以直接用計算機計算）
其實這條題目已經給了你提示，就是用(a)部分的結果來計算，下次遇到同類題目時可不要再想不到喔。 還有問題的話可以問我！

(a) 2y = 4x + 1    x = (y/2) - (1/4) -------- (i)    16x2 + 4y2 - 4y = 5 --(ii)
Sub. (i) into (ii), 16[(y/2) - (1/4)]2 + 4y2 - 4y = 5 8y2 - 8y - 4 = 0 y = -0.366 or y = 1.37 (Correct to 3 sig. fig.)
Sub y = -0.366 into (i), x = [(-0.366)/2] - (1/4) x = -0.433 (Correct to 3 sig. fig.)
Sub. y = 1.37 into (i), x = [(1.37)/2] - (1/4) x = 0.433 (Correct to 3 sig. fig.)
∴ (x,y) = (-0.433, -0.366) or (x,y) = (0.433, 1.37) //
(b) Put x = (sinθcosθ) and y = (sinθ+cosθ) in (a), ∴ (sinθcosθ) = 0.433, (sinθ+cosθ) = 1.37 or (sinθcosθ) = -0.433, (sinθ+cosθ) = -0.366 [1]

When (sinθcosθ) = 0.433 , sin2θ = 0.217 (Correct to 3 sig. fig.) i.e. sin2θ = 2sinθcosθθ = 30o or θ = 60o or θ = 210o (rejected) or θ = 240o (rejected) i.e. 要檢查答案[1]
When (sinθcosθ) = -0.433 , sin2θ = -0.217 (Correct to 3 sig. fig.) θ = 120o (rejected) or θ = 150o or θ = 300o or θ = 330o (rejected)
∴θ = 30o or θ = 60o or θ = 150o θ = 300o//

而樓上的方法呢，也沒有問題，只是由於他沒有督機，計出來的是開方的答案，所以可以輕易地拆做兩個數，只是最後他發了瘋··· cosθ = 1/2, θ絕對是300o 而不是330o！現在我提供另一個方法：

(b) Let sinθ and cosθ be the roots of the below two equation: i.e. 有sum of roots 和 product of roots就可以form一條equation了
x2-1.37x+0.433 = 0 ------(iii)
x2+0.366x-0.433 = 0 ------(iv)

From (iii), x = 0.866 (Correct to 3 sig. fig) or x = 0.5
From (iv), x = -0.866 (Correct to 3 sig. fig) or x = 0.5
Hence, i.e. 這裡我為了清晰點才隔行的
sinθ = 0.866, cosθ = 0.5 or
sinθ = -0.866, cosθ = 0.5 or
sinθ = 0.5, cosθ = 0.866 or
sinθ = 0.5, cosθ = -0.866

θ = 60o or θ = 300o or θ = 30o or θ = 150o // i.e. 沒有要rejected的，所以可以直接答案

suggested solution:


圖片參考：http://imgcld.yimg.com/8/n/HA08446686/o/20130105204511.jpg