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!

Sines are positive in the first and second quadrants.
So 2x-1= .2526 or pi-.2426 or 2pi+.2526 or 3pi-.2426 etc
So a formula for these answers is npi+(-1)^n(.2526)

Thanks! I think what I was missing was I trying x= pi-.2526, ignoring the 2x-1 for some reason. But I've got the idea now.