Okay, I have to find all solutions to the equation and I'm stuck.
$\displaystyle sin(x + pi/4) = 1/2$
I unno what to do. Should I move that pi/4 to the right?
Okay, I know that there are two possible solutions to this that being 30 degrees and 330 degrees. I don't understand where that 2kpi is coming from though. Is that like the same thing as 2pi being one circle while k is how many times it should loop? Anywho, I'm still confused over this. I got the answer by subtracting pi/4 from pi/6 and 5pi/6, which would make it -pi/12 and 7pi/12.
$\displaystyle \sin{\left(x + \frac{\pi}{4}\right)} = \frac{1}{2}$
$\displaystyle x + \frac{\pi}{4} = \arcsin{\left(\frac{1}{2}\right)}$
$\displaystyle x + \frac{\pi}{4} = \left\{\frac{\pi}{6},\pi - \frac{\pi}{6}\right\} + 2\pi n$ where n is an integer, since sine is positive in the first and second quadrants.
$\displaystyle x + \frac{\pi}{4} = \left\{\frac{\pi}{6}, \frac{5\pi}{6}\right\} + 2\pi n$
$\displaystyle x = \left\{\frac{\pi}{6}, \frac{5\pi}{6}\right\} + 2\pi n - \frac{\pi}{4}$.
Can you go from here?