Question 252482
Here is the original equation:
4*sin^2(x) + 1= -4*sin(x)
First we want to set it = 0.
4*sin^2(x) + 4*sin(x) +1 = 0
Let sin(x) = U; this is a generic dummy variable to make the problem easier to solve.
{{{4U^2 + 4U  + 1 = 0}}}
Now we factor as normal to get
{{{(2U+1)(2U+1) = 0}}}
Solving for u, we get
{{{U = -1/2}}}
Remember we used U as a dummy variable. We have to resubstitute sin(X) back in as
{{{sin(x) = -1/2}}}
We want to know what X values may the sin -1/2. The sign will be -1/2 at X = 150 degrees and 210 degrees. In radians, X = 5pi/6 and 7pi/6.