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So, I thought I had this down, but I guess not.
The equation is cos2x = 1/2 [0, 2pi)
What I do is think what angle has a cosine of 1/2, then I divide it by 2 to get x.
60 degrees, or pi/3 has a cos of 1/2, so x = 30 degrees or pi/6
Because the 1/2 is positive, I know that x is in quadrant I and IV, so I think of the reference angles of 30 degrees, which are 30 (quadrant I, duh) and 330 degrees or 11pi/6.
The final answers that I get are pi/6 and 11pi/6, but my book has 5pi/6 and 7pi/6 which would be in quadrants II and III respectively. Cos is negative in quadrants II and III, so I don't understand how there are solutions in these quadrants to the original equation.
Any help is appreciated.
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