SOLUTION: find all solutions in the interval [0,2pi) for the equation 3csc x-4sin x=0.

Question 788739: find all solutions in the interval [0,2pi) for the equation 3csc x-4sin x=0.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
does not exist when at and
For any other values of , we can transform the equation into an equivalent quadratic equation by multiplying times :
<-->-->
-->-->
The solutions come from
and

In the interval

--> ( and being a supplementary angle has the same sine)
and --> (Those are co-terminal angles of and , found adding to and )

NOTE:
For this kind of equation, a change of variable often helps to see the equation as a quadratic equation.
It is easier to see as a quadratic equation using the change of variable .
In this case, it was easy to solve the problem, even without mentioning a quadratic equation. In other cases, solving the quadratic may be more complivcated, so making the change of variable may save confusion and ink.
We get
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