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(52824)   (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.
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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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