I need to find the intersections of 3sin(2x) and y=2. I can expand sin(2x) with a double angle formula but I'm not getting the answers. The range is 0 - 360.
since $\displaystyle 0 < x < 360$
$\displaystyle 0 < 2x < 720$
$\displaystyle 3\sin(2x) = 2$
$\displaystyle \sin(2x) = \frac{2}{3}$
$\displaystyle 2x = \arcsin\left(\frac{2}{3}\right)$
$\displaystyle 2x = 180 - \arcsin\left(\frac{2}{3}\right) $
$\displaystyle 2x = 360 + \arcsin\left(\frac{2}{3}\right)$
$\displaystyle 2x = 540 - \arcsin\left(\frac{2}{3}\right)$
solve for $\displaystyle x$ in all four equations