Question #ec712

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Answer 1 · 2017-01-03T22:45:46

See below.

#2cos theta = 1# only if #cos theta = 1/2#

Going through the special angles, we know that

#cos 0 = 1#

#cos(pi/6) = sqrt3/2#

#cos(pi/4) = sqrt2/2#

#cos(pi/3) = 1/2#

So there is our first solution.

Continuing once around the circle (#0 <= theta < 2pi#) we get another solution at #x = (5 pi)/3#.

So the solutions are

#pi/3# and #(5pi)/3#.