Thread: Symmetry solutions intersecting a sinusoidal function.

Set f(x) = g(x) and find the principal and
symmetry solutions.

f(x) = sin (2x − 1), g(x) = 1/4.

So I have no trouble finding the principal solution...

sin(2x-1)=1/4
2x-1=.2526
2x=1.2526
x=.6263

Now how on earth do I about solving for the symmetry solution without cheating using a graph? I know, or at least think, you have to relate it to a minimum or maximum, but this becomes difficult without a graph because I'm not entirely sure where the solution I have is located. How do you solve this with just plain equations? I'm reviewing precalc/calc after a 5 year hiatus and only have myself and an old text book and the text book isn't much for help.

Thanks!