How do you solve #1 - cos(x) = 1/2# from #[0,2pi]#?

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How do you solve #1 - cos(x) = 1/2# from #[0,2pi]#?

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Answer 1 · 2015-10-01T13:58:01

#S = {pi/3, (5pi)/3}#

Explanation:

Isolate the cosine

#-cos(x) = 1/2 - 1#
#-cos(x) = -1/2#
#cos(x) = 1/2#

We know the cosine is #1/2# when we have #x = pi/3#, however, the cosine is also positive on the fourth quadrant, so another possible value of #x# is #x = 2pi - pi/3 = (6pi - pi)/3 = (5pi)/3#

Thus we have a set of solutions #S# such that #S = {pi/3, (5pi)/3}#

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How do you solve #1 - cos(x) = 1/2# from #[0,2pi]#?

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