How do you solve $2 {cos}^{2} x - cos x = 0$ $2 cos^2 x - cos x = 0$ from [0,360]?

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Answer 1 · 2015-10-01T13:53:55

$S = {60º,90º,270º,300º}$

Factor the cosine out

$cosx(2cosx - 1) = 0$

So either must be zero for this to apply, we have

$cosx = 0 rarr x = 90º or 270º$

Or

$2cosx - 1 = 0 rarr cosx = 1/2$
$x = 60º or 300º$

We know those values because they're on your standard unit circle / they're special cosine values / special angles.

Thus, the set of solutions $S$ is $S = {60º,90º,270º,300º}$

How do you solve 2 cos^2 x - cos x = 02cos2x−cosx=02 cos^2 x - cos x = 0 from [0,360]?