1. We are asked to solve the trigonometric equations for $x$ where $\sin x$, $\cos x$, or $\tan x$ equals given values. 2. The general solutions for sine, cosine, and tangent equations are: - For $\sin x = a$, solutions are $x = \arcsin(a) + 2k\pi$ or $x = \pi - \arcsin(a) + 2k\pi$ for any integer $k$. - For $\cos x = a$, solutions are $x = \arccos(a) + 2k\pi$ or $x = -\arccos(a) + 2k\pi$ for any integer $k$. - For $\tan x = a$, solutions are $x = \arctan(a) + k\pi$ for any integer $k$. 3. We solve the first equation only as per instructions: (i) $\sin x = \frac{1}{2}$ 4. Using the unit circle, $\sin x = \frac{1}{2}$ at $x = \frac{\pi}{6}$ and $x = \frac{5\pi}{6}$ within one period $[0, 2\pi)$. 5. The general solution is: $$ x = \frac{\pi}{6} + 2k\pi \quad \text{or} \quad x = \frac{5\pi}{6} + 2k\pi, \quad k \in \mathbb{Z} $$ 6. This means $x$ can be any angle coterminal with $\frac{\pi}{6}$ or $\frac{5\pi}{6}$. Final answer: $$ x = \frac{\pi}{6} + 2k\pi \quad \text{or} \quad x = \frac{5\pi}{6} + 2k\pi, \quad k \in \mathbb{Z} $$