1. The problem is to graphically solve the equation $\sin x = \cos x$. 2. To find where $\sin x = \cos x$, we can rewrite this as $\sin x - \cos x = 0$. 3. Consider the function $f(x) = \sin x - \cos x$ and find where it intersects the $x$-axis. 4. Equivalently, $\sin x = \cos x$ means $\tan x = 1$ because dividing both sides by $\cos x$ (where $\cos x \neq 0$) gives $\tan x = 1$. 5. The general solutions to $\tan x = 1$ are $x = \frac{\pi}{4} + n\pi$, where $n$ is any integer. 6. We can plot $y=\sin x$ and $y=\cos x$, and visually identify the points where their graphs intersect, which are at $x = \frac{\pi}{4} + n\pi$. 7. The graph will show that these two functions cross periodically at these points. Final answer: All solutions to $\sin x = \cos x$ are $x = \frac{\pi}{4} + n\pi$, $n \in \mathbb{Z}$.