Question

The principle solutions of $\sin \theta =-\frac{1}{2}$ are

• A. $\pi /4$
• B. $11\pi /6$
• C. $\pi /3$
• D. $\frac{7\pi }{6}$

Answer 1

Answer: (B), (D)

$11\pi /6$
$\frac{7\pi }{6}$

The principle solution is the solution of trignometric angle in [0,2$\pi$]

So There are two principle solutions ($\pi$+$\frac{\pi }{6}$) and ($2\pi$-$\frac{\pi }{6}$)=$\frac{7\pi }{6}$ and $\frac{11\pi }{6}$