How do you solve #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}#