Solve the equation:
2 cos² x + 5 sin x + 1 = 0, 0 <= x < 360°
(giving your answer in degrees).
Okay, I noticed that if I subtracted 2 into both sides, then part of the LHS will become '2 cos² x - 1', which I know is identical to 'cos 2x'.
cos 2x + 5 sin x = -2
Now however, I'm not sure where to go next.
I'm kind of aiming to get it into the form 'R cos (x - alpha)', and go from there. But am stuck on what to do with this '2x' in the cos term.
I thought that I could use the Half-angle formulae, but this seems to take me round to cos 2x again.. :(