Trigonometry - compound angles
2008-03-09 7:17 pm
The quadratic equation in x, x^2 - 2開方2x sin(C- 3.14/4) + cos4C = 0 has repeated roots. Find the general values of C
回答 (1)
2008-03-09 8:07 pm
✔ 最佳答案
Discriminant of the equation = 0, so[-2√2 sin (C - π/4)]2 - 4(1)(cos 4C) = 0
8 sin2 (C - π/4) - 4 cos 4C = 0
4 [1 - cos 2(C - π/4)] - 4 cos 2(2C) = 0
4 - 4 cos (2C - π/2) - 4(1 - 2sin2 2C) = 0
4 - 4 sin 2C - 4 + 8sin2 2C = 0
2sin2 2C - sin 2C = 0
sin 2C (2 sin 2C - 1) = 0
sin 2C = 0 or 1/2
2C = nπ or nπ + (-1)nπ/6
C = nπ/2 or nπ/2 + (-1)nπ/12
參考: My Maths knowledge
收錄日期: 2021-04-14 19:46:49
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