Elementary trigonometric equation

Text

Solve the equation $2\sin x-1=0$ in the interval $[0^\circ,\,360^\circ)$.

Solution

Isolate the sine: $\sin x=\dfrac12$. On the unit circle the value $\tfrac12$ is taken by the sine at two points, in the first and second quadrants: $x=30^\circ\qquad\text{and}\qquad x=180^\circ-30^\circ=150^\circ.$ $\boxed{\,x=30^\circ\quad\lor\quad x=150^\circ\,}$