Rearranging yields
#sin^2(x) = 1/4#.
#sin(x) = +-1/2#.
Now, we must simply find the solutions to this sine function.
We know that the sine of 30 degrees (#pi/6# radians) satisfies the positive equality, so we can simply apply this to all 4 quadrants. For example, possible solutions include #pi/6, (5pi)/6, (7pi)/6, (11pi)/6, (13pi)/6#, so on and so forth. Thus, we can express our answer as #{x|x in pi/6 + pik or (5pi)/6 + pik}#, where #k in ZZ#. Simply put, there are an infinite number of solutions to this equation, and we must use an arbitrary variable #k# to denote this.
