How do you find the exact value of sin^-1(1/2)?

$\theta = {30}^{\circ} + 360 {n}^{\circ} , \mathmr{and} \theta = {150}^{\circ} + 360 {n}^{\circ}$.
You are looking for an angle whose opposite side is 1 and hypotenuse is 2. That triangle is the ${30}^{\circ} - {60}^{\circ} - {90}^{\circ}$ triangle. Therefore, the angle that is opposite from 1 is $\theta = {30}^{\circ}$. But since sine is positive in quadrants I and II it means that we will have two sets of answers. That is, $\theta = {30}^{\circ} + 360 {n}^{\circ} , \mathmr{and} \theta = {150}^{\circ} + 360 {n}^{\circ}$.