Question 784570: how do you solve for x algebraically for : 2sin^2x+5sinx=3
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! 
If you make a change of variable, it gets easier to write and easier to see the solution.
Substititing  , the equation turns into
You probably know what to do with that equation.
I would do this:
-->  --> 
From that last, factored equation, we get two solutions in terms of  :
 -->  -->  and
 --> 
In terms of  ,  makes no sense.
On the other hand, from the other value we get many values for
To begin with, if we just stick to the first turn, with  , we have 2 solutions:  and  , because
 and 
If using radians rather than degrees, for  , the soluttions are  and  , because
 and 
If you are not restricted to the first turn, there are infinite solutions, because co-terminal angles have the same trigonometric function values, so that all the solutions could be written as
 or  for any integer  .
(Making  gives you the solutions in the first turn).
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