Find all angles between 0 degrees and 360 degrees which satisfy the equation:
cos 2x+ sin 66° =0
2007-07-29 23:48:43 · 3 answers · asked by Stormy Knight 1 in Science & Mathematics ➔ Mathematics
cos 2x + sin 66 = 0
Therefore,
cos 2x = - sin 66
cos 2x = -0.913545.....
2x = 156 or 204 or 516 or 564
Therefore the only angles between 0 and 360 which satisfy the given equation are:
x = 78 degrees, x = 102 degrees, x = 258 degrees,
and x = 282 degrees.
2007-08-02 23:44:57 · answer #1 · answered by iqof300 3 · 0⤊ 0⤋
sin y = cos (90 - y)
so cos2x + cos (90 - 66) = 0
so cos2x + cos 24 = 0
so cos2x = -cos 24
now because -cos y = cos (180 - y)
cos 2x = cos 156
so 2x = 156
and also 2x = 360 - 156 = 204
so values for 2x in range up to 720 (double range because 2x)
2x = 156, 204, 516, 564
x = 78, 102, 258, 282
2007-07-30 00:07:44 · answer #2 · answered by JAMES C 2 · 1⤊ 2⤋
cos 2x = 0.914
2x = 24° , 336° , 384° , 696°
x = 12° , 168° , 192° , 348°
2007-07-30 03:20:03 · answer #3 · answered by Como 7 · 1⤊ 1⤋