Question

How many solutions does sin(4x) = ½ have on the interval of (0, 2 pi]

Answer 1

`\sin(4x)=\cfrac{1}{2}\implies 4x=\sin^(-1)\left( \cfrac{1}{2} \right) \\\\\\ 4x=\cfrac{\pi }{6}~~,~~\cfrac{5\pi }{6} \implies x=\cfrac{\pi }{24}~~,~~\cfrac{5\pi }{24}\qquad \begin{array}{llll} \textit{two solutions}\\ \textit{on the range of }(0,2\pi ] \end{array}`