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二倍角問題
發問:
唔該 (sin θ)^4+(cos θ)^4=sin 2θ, find θ.
最佳解答:
As follows: 圖片參考：http://i238.photobucket.com/albums/ff245/chocolate328154/Maths136.jpg?t=1201186639 2008-01-24 23:03:34 補充： Then in the range 0
其他解答:
(sin θ)^4 + (cos θ)^4 = sin 2θ ( (sin θ)^2 + (cos θ)^2 )^2 - 2 (sin θ)^2 (cos θ)^2 = sin 2θ ( (sin θ)^2 + (cos θ)^2 )^2 - (sin 2θ)^2 / 2 = sin 2θ 1 - (sin 2θ)^2 / 2 = sin 2θ 2 - (sin 2θ)^2 = 2 sin 2θ (sin 2θ)^2 + 2 sin 2θ - 2 = 0 sin 2θ = ( -2 + sqrt(4 + 8) ) / 2 or sin 2θ = ( -2 - sqrt(4 + 8) ) / 2 sin 2θ = -1 + sqrt(3) or sin 2θ = -1 - sqrt(3) (rejected) sin 2θ = -1 + sqrt(3) θ = 23.5293 deg. 2008-01-24 23:05:42 補充： my god, 比人食胡先,請投我一票, 好重要架
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