Question #7a9e2

1 Answer
Dec 17, 2017

{x|x in pi/6 + pik or (5pi)/6 + pik}

Explanation:

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.