Maths

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, .......