Posted by Bob on Tuesday, January 29, 2013 at 9:52pm.
I don't know if you are supposed to do this by simply substiting, or actually solve the equation.
I will solve it
2sinx + 4cos 2x = 3
2sinx + 4(1 - 2sin^2 x) -3=0
2sinx + 4 -8sin^2 x - 3 = 0
8sin^2 x - 2sinx -1 = 0
sinx = (2 ± √36)/16 = 1/2 or -1/4
x = 30° or 150° or x = 194.4775..° or 345.522°
so to the nearest degree I got
x = 30, 150, 194 and 346
I see only two of these in your list, so the others don't work
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