Which of the following is a general solution of the equation sin 2x = -rac{1}{2}? A - HSC - SSCE Mathematics Extension 1 - Question 11 - 2018 - Paper 1

To solve the equation $\sin(2x) = -\frac{1}{2}$, we first find the angles which satisfy this condition. The sine function equals -1/2 at certain reference angles in the unit circle. These reference angles can be obtained from the sine function:

1. The angles are given by:

   • $2x = \frac{7\pi}{6} + 2n\pi$
   • $2x = \frac{11\pi}{6} + 2n\pi$

2. Dividing both sides of the equations by 2 gives:

   • $x = \frac{7\pi}{12} + n\pi$
   • $x = \frac{11\pi}{12} + n\pi$

This can be summarized in a general solution form depending on whether n is even or odd for the possible solutions.