Question 924330: Please solve the following equation.
(Enter your answers as a comma-separated list. Let k be any integer. Enter DNE is there is no solution.)
2 cos 2θ − 1 = 0
(a) Find all solutions of the equation.
θ =
(b) Find the solutions in the interval [0, 2π).
θ =
Thanks
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Part a)
Solve for 
 or  where k is any integer.
 or 
 or 
The general solutions are or where k is any integer.
You can condense that into one equation:  (take note of the plus/minus)
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Part b)
We'll find the first set of solutions.
Plug in integer values of k into to generate solutions. Make sure you are between  and  roughly.
Plug in 
This is in the interval [0,2pi), so we keep it.
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Plug in 
This is in the interval [0,2pi), so we keep it.
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Plug in 
we have gone over 6.28, so we stop here and we don't include this solution because it is not in the interval [0,2pi)
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Now we move onto the second part.
Plug in integer values of k into to generate solutions. Make sure you are between and roughly.
Plug in
That is less than x = 0, so we toss out this solution.
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Plug in
This is in the interval [0,2pi), so we keep it.
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Plug in
This is in the interval [0,2pi), so we keep it.
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Plug in 
we have gone over 6.28, so we stop here and we don't include this solution because it is not in the interval [0,2pi)
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The exact solutions to part b) are  ,  ,  ,  . They are exact solutions in terms of 
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Let me know if that helps or not. Thanks.
If you need more help, feel free to email me at jim_thompson5910@hotmail.com
My Website: http://www.freewebs.com/jimthompson5910/home.html
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