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標題:

Maths

發問:

Find the general solution of 6 cos 2x + 8 sin 2x = 9

最佳解答:

Transform 6 cos 2x + 8 sin 2x to Rcos(2x - a) = Rcos 2x cos a + Rsin 2x sin a That is R cos a = 6 .........(1) and R sin a = 8 ...........(2) so R = sqrt (36 + 64) = 10 a = arc tan ( 8/6) = 53.13 degree. The equation becomes 10 cos (2x - 53.13) = 9 so 2x - 53.13 = arc cos (9/10) = 25.84 degree General solution : 2x - 53.13 = 2nπ +/- 25.84 x = nπ +/- 12.92 + 26.56 x = 13.64, 39.48, 193.64, 219.48, ........ 2012-11-21 08:51:19 補充： x can also be written as : x = nπ + 39.48 or x = nπ + 13.64. n = 0,1,2,3, .......

其他解答:C8D74AB62542840B