it is given that F(Θ)=2sin^3Θ+sin^2Θ-5sinΘ+2.
(a) let G(x) denote the polynomial for rewriting F(Θ) where x=sin Θ
find G(-2).hence factorize G(x)
(b) use the result of (a) to solve the equation F(Θ)=0 for 0゜≦Θ≦360°,correct to the nearest degree.
點解AND 點做?
maths f4
2011-06-05 7:39 am
回答 (1)
2011-06-05 9:01 am
✔ 最佳答案
(a) Just follows the instruction is OKx = sinΘ
G(X) = 2x^3 + x^2 - 5x + 2
G(-2) = -16 + 4 + 10 + 2 = 0
(b) G(x) = (x + 2)(2x^2 - 3x + 1)
=> roots og G(x) are x = -2, (3±1)/4 or x = -2, 1, 1/2
F(Θ) = 0 => sinΘ = 1 or 1/2 and so Θ = 90, 30, 150
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