sin1°是不是代数数

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2026-03-08 21:14:00

发布于：浙江

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sin⁡3∘=18[3(1+5)−2(5−5)]A=sin⁡3∘sin⁡3θ=3sin⁡θ−4sin⁡3θθ=1∘B=sin⁡1∘A=3B−4B3−4B3+3B−A=04B3−3B+A=0由于A是代数数，所以B是代数数\sin{3^\circ}=\frac18[\sqrt3(1+\sqrt5)-\sqrt2(5-\sqrt5)]\\ A=\sin{3^\circ}\\ \sin{3\theta}=3\sin{\theta}-4\sin^3{\theta}\\ \theta=1^\circ\\ B=\sin{1^\circ}\\ A=3B-4B^3\\ -4B^3+3B-A=0\\ 4B^3-3B+A=0\\ 由于A是代数数，所以B是代数数
这里让你看一下B的方程表示：
281474976710656x48−3377699720527872x46+18999560927969280x44−66568831992070144x42+162828875980603392x40−295364007592722432x38+411985976135516160x36−452180272956309504x34+396366279591591936x32−280058255978266624x30+160303703377575936x28−74448984852135936x26+28011510450094080x24−8500299631165440x22+2064791072931840x20−397107008634880x18+59570604933120x16−6832518856704x14+583456329728x12−35782471680x10+1497954816x8−39625728x6+579456x4−3456x2+1=0281474976710656x^{48} - 3377699720527872x^{46} + 18999560927969280x^{44} -66568831992070144x^{42} + 162828875980603392x^{40} - 295364007592722432x^{38} + 411985976135516160x^{36} - 452180272956309504x^{34} + 396366279591591936x^{32} - 280058255978266624x^{30} + 160303703377575936x^{28} - 74448984852135936x^{26} + 28011510450094080x^{24} - 8500299631165440x^{22} + 2064791072931840x^{20} - 397107008634880x^{18} + 59570604933120x^{16} - 6832518856704x^{14} + 583456329728x^{12} - 35782471680x^{10} + 1497954816x^8 - 39625728x^6 + 579456x^4 - 3456x^2 + 1 = 0

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