SOLUTION: how do you solve for x algebraically for : 2sin^2x+5sinx=3

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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