Inverse Trigonometric Functions Math Example 4

Solution

1. 1
   Isolate: $\sin(x)=\frac{1}{2}$. Primary solution: $x=\arcsin\!\left(\frac{1}{2}\right)=\frac{\pi}{6}$.
2. 2
   Second solution: sine is also $\frac{1}{2}$ in the second quadrant at $x=\pi-\frac{\pi}{6}=\frac{5\pi}{6}$.
3. 3
   So $x=\frac{\pi}{6}$ and $x=\frac{5\pi}{6}$. The $\arcsin$ function only gives the first; the second must be found using symmetry.