1. Let's start by stating the problem: solving a trigonometric equation means finding all angles $x$ that satisfy an equation involving trigonometric functions like $\sin x$, $\cos x$, or $\tan x$. 2. For example, consider the equation $\sin x = \frac{1}{2}$. 3. We want to find all angles $x$ such that the sine of $x$ equals $\frac{1}{2}$. 4. Recall that $\sin x = \frac{1}{2}$ at $x = \frac{\pi}{6} + 2k\pi$ and $x = \frac{5\pi}{6} + 2k\pi$ for any integer $k$, because sine is positive in the first and second quadrants. 5. Therefore, the general solutions are: $$ x = \frac{\pi}{6} + 2k\pi \quad \text{or} \quad x = \frac{5\pi}{6} + 2k\pi, \quad k \in \mathbb{Z} $$ 6. This method applies to other trigonometric equations: isolate the trig function, find reference angles, and use the unit circle to find all solutions. 7. If you have a specific trigonometric equation, please provide it, and I can solve it step-by-step!