Coming up with a formula for the answers to a sin(x) sequence.

Question

So I've already done the grunt work and solved a trigonometric equation, the solutions to the equation are when x = pi/6, 5pi/6, 7pi/6, 11pi/6, 13pi/6 17pi/6.... etc I think you should understand the pattern by now. I want to come up with an equation that summarizes the pattern where k = integer. Now I was planning on using the formula for an arithmetic sequence but the problem is there isn't a single common difference, there's two in this case. I know I can make 2 separate formulas to fix this but I was wondering if there was a way to come up with a single equation and if so, what is it?

Answer 1

If sin²x = 1/4, then sinx = ± 1/2.

If sinx = 1/2, then x = π/6, 5π/6, 13π/6, 17π/6, ...

If sinx = -1/2, then x = 7π/6, 11π/6, 19π/6, 23π/6, ...