SOLUTION: Hello! I need help solving this please. Find all solutions of the equation in the interval [0, 2π): 24 sin2 x = 24 − 12 cos x Please explain each step. Thank

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Question 978216: Hello!
I need help solving this please.
Find all solutions of the equation in the interval [0, 2π):
24 sin2 x = 24 − 12 cos x
Please explain each step.
Thank you
Answer by KMST(5328)   (Show Source): You can put this solution on YOUR website!
I am assuming that the equation is .
I would divide both sides of the equation by to get a friendlier equivalent equation:
--->---> .
Then, using the fact that
<---> ,
I would re-write as
,
and then I would just write for to save ink.
With the "change of variable" , I save ink and confusion:
looks a lot easier on the eyes.
Now, I solve:




That last equation would traditionally be written as
, and is a "quadratic equation".
Quadratic equations can be solved by "completing the square" or by using the quadratic formula.
In certain cases, they can also be solved by factoring,
and are that lucky in this case. Factoring we get
--->--->---> .
In the interval with ,
---> and --->
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