SOLUTION: An equation is given. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate. If there is no solution, enter NO

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Question 1102804: An equation is given. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.)
2 cos(2θ) + 1 = 0
Find all solutions within the interval (0, 2pi).

Answer by ikleyn(52832)   (Show Source): You can put this solution on YOUR website!
.
 + 1 = 0  ====>


 =   ====>


  may have one of the two values:   =   or   = .


Case 1.  If   = ,  then the solutions for  in the interval  [0,)  are  these TWO values:

          =    and/or    =  = .



Case 2.  If   = ,  then the solutions for  in the interval  [0,)  are  these TWO values:

          =    and/or    =  = .


Answer.  The given equation has 4 (four, FOUR) solutions in the interval  [0,):

                ,  ,  ,  and  .


The plot below visually confirms existing of 4 solutions:



Plot y =


        SOLVED.


----------------
N O T E. All the part of the condition  IN PARENTHESES  makes no sense  and  IS NOT RELEVANT  to the problem at all.


        When I see such a  NONSENSE  in the condition,  I become sad,
        because I clearly see that the person who prepared this post  does not understand WHAT HE IS WRITING.



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