Trigonometric equations, in general, have an unlimited number of solutions. Usually the domain is restricted to 0 ≤ θ ≤ 360, to limit the number of solutions.
No general method for solving equations can be given. However, the following suggestions will be helpful.
1) Reduce the equation to a simpler equation by factoring, if possible.
2) Simplify the functions of different angles to functions of the same angle by means of known formulas.
3) Simplify the equation so that it involves only the same function of the angle.
4) Check your answers.
2 cos2 x = – 3 cos x + 2 for x, 0° ≤ x < 360°
2 cos2 x = – 3 cos x + 2
2 cos2 x + 3 cos x – 2 = 0
(2 cos x – 1)(cos x + 2) = 0
2 cos x – 1 = 0
x = 60°, 300°
cos x + 2 = 0
cos x = –2
x = Ø
Therefore, x = 60°, 300°
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